Context-free languages can be described using context-free grammars, which are recursive rules that generate strings in a language. An example grammar is presented that generates strings of 1s and 0s separated by # symbols. Context-free grammars consist of variables, terminals, rules with variables on the left-hand side replacing with strings on the right-hand side, and a starting variable. Context-free languages can be recognized by pushdown automata using an extra stack. Regular languages are a subset of context-free languages. Context-free languages have closure properties including union, concatenation, and homomorphism. Derivation trees can represent grammar derivations and Backus-Naur form is a notation for compactly representing
Context free grammars (CFGs) are formal systems that describe the structure of languages. A CFG consists of variables, terminals, production rules, and a start variable. Production rules take the form of a single variable producing a string of terminals and/or variables. CFGs can capture the recursive structure of natural languages while ignoring agreement and reference. They are used to define context-free languages and generate parse trees. Ambiguous grammars have sentences with multiple parse trees, and disambiguation aims to impose an ordering on derivations. While ambiguity cannot always be eliminated, simplifying and restricting grammars has theoretical and practical benefits.
This document provides an overview of deterministic finite automata (DFA) through examples and practice problems. It begins with defining the components of a DFA, including states, alphabet, transition function, start state, and accepting states. An example DFA is given to recognize strings ending in "00". Additional practice problems involve drawing minimal DFAs, determining the minimum number of states for a language, and completing partially drawn DFAs. The document aims to help students learn and practice working with DFA models.
Context-free grammars are a notation for describing languages using variables and productions. They are more powerful than regular expressions but still cannot define all possible languages. A context-free grammar consists of terminals, variables, a start symbol, and productions. Strings in the language are derived by replacing variables according to productions until only terminals remain. Leftmost and rightmost derivations restrict replacements to specific variables.
This document provides an introduction to automata theory and finite automata. It defines an automaton as an abstract computing device that follows a predetermined sequence of operations automatically. A finite automaton has a finite number of states and can be deterministic or non-deterministic. The document outlines the formal definitions and representations of finite automata. It also discusses related concepts like alphabets, strings, languages, and the conversions between non-deterministic and deterministic finite automata. Methods for minimizing deterministic finite automata using Myhill-Nerode theorem and equivalence theorem are also introduced.
The document discusses finite automata and deterministic finite automata (DFAs) in particular. It defines DFAs using a 5-tuple notation and explains that a DFA has a single possible state transition for each input symbol. The document provides examples of constructing DFAs to recognize specific languages and describes the step-by-step process of using a DFA to determine if a string is accepted by the language. It also gives examples of building DFAs for languages containing certain substrings and strings with a minimum length.
This document discusses the Chomsky hierarchy and different types of automata and grammars. It begins by describing applications of different automata like Turing machines, linear bounded automata, pushdown automata, and finite automata. It then discusses recursive and enumerable sets and linear bounded automata. It provides examples of languages accepted by LBAs and notes that LBAs have more power than PDAs but less than TMs. It also discusses unrestricted grammars, context-sensitive grammars, and places language classes in the Chomsky hierarchy. It concludes by asking questions about left linear versus right linear grammars.
Syntax analysis is the second phase of compiler design after lexical analysis. The parser checks if the input string follows the rules and structure of the formal grammar. It builds a parse tree to represent the syntactic structure. If the input string can be derived from the parse tree using the grammar, it is syntactically correct. Otherwise, an error is reported. Parsers use various techniques like panic-mode, phrase-level, and global correction to handle syntax errors and attempt to continue parsing. Context-free grammars are commonly used with productions defining the syntax rules. Derivations show the step-by-step application of productions to generate the input string from the start symbol.
Context free grammars (CFGs) are formal systems that describe the structure of languages. A CFG consists of variables, terminals, production rules, and a start variable. Production rules take the form of a single variable producing a string of terminals and/or variables. CFGs can capture the recursive structure of natural languages while ignoring agreement and reference. They are used to define context-free languages and generate parse trees. Ambiguous grammars have sentences with multiple parse trees, and disambiguation aims to impose an ordering on derivations. While ambiguity cannot always be eliminated, simplifying and restricting grammars has theoretical and practical benefits.
This document provides an overview of deterministic finite automata (DFA) through examples and practice problems. It begins with defining the components of a DFA, including states, alphabet, transition function, start state, and accepting states. An example DFA is given to recognize strings ending in "00". Additional practice problems involve drawing minimal DFAs, determining the minimum number of states for a language, and completing partially drawn DFAs. The document aims to help students learn and practice working with DFA models.
Context-free grammars are a notation for describing languages using variables and productions. They are more powerful than regular expressions but still cannot define all possible languages. A context-free grammar consists of terminals, variables, a start symbol, and productions. Strings in the language are derived by replacing variables according to productions until only terminals remain. Leftmost and rightmost derivations restrict replacements to specific variables.
This document provides an introduction to automata theory and finite automata. It defines an automaton as an abstract computing device that follows a predetermined sequence of operations automatically. A finite automaton has a finite number of states and can be deterministic or non-deterministic. The document outlines the formal definitions and representations of finite automata. It also discusses related concepts like alphabets, strings, languages, and the conversions between non-deterministic and deterministic finite automata. Methods for minimizing deterministic finite automata using Myhill-Nerode theorem and equivalence theorem are also introduced.
The document discusses finite automata and deterministic finite automata (DFAs) in particular. It defines DFAs using a 5-tuple notation and explains that a DFA has a single possible state transition for each input symbol. The document provides examples of constructing DFAs to recognize specific languages and describes the step-by-step process of using a DFA to determine if a string is accepted by the language. It also gives examples of building DFAs for languages containing certain substrings and strings with a minimum length.
This document discusses the Chomsky hierarchy and different types of automata and grammars. It begins by describing applications of different automata like Turing machines, linear bounded automata, pushdown automata, and finite automata. It then discusses recursive and enumerable sets and linear bounded automata. It provides examples of languages accepted by LBAs and notes that LBAs have more power than PDAs but less than TMs. It also discusses unrestricted grammars, context-sensitive grammars, and places language classes in the Chomsky hierarchy. It concludes by asking questions about left linear versus right linear grammars.
Syntax analysis is the second phase of compiler design after lexical analysis. The parser checks if the input string follows the rules and structure of the formal grammar. It builds a parse tree to represent the syntactic structure. If the input string can be derived from the parse tree using the grammar, it is syntactically correct. Otherwise, an error is reported. Parsers use various techniques like panic-mode, phrase-level, and global correction to handle syntax errors and attempt to continue parsing. Context-free grammars are commonly used with productions defining the syntax rules. Derivations show the step-by-step application of productions to generate the input string from the start symbol.
Finite Automata: Deterministic And Non-deterministic Finite Automaton (DFA)Mohammad Ilyas Malik
The term "Automata" is derived from the Greek word "αὐτόματα" which means "self-acting". An automaton (Automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically.
This document discusses Noam Chomsky's hierarchy of formal languages. It introduces Chomsky's classification of formal languages from Type-0 to Type-3 based on the type of grammar that generates them. Type-0 languages are the most powerful, being generated by unrestricted grammars and equivalent to Turing machines. Type-3 languages are the simplest, being generated by regular grammars and equivalent to finite state automata. Examples are provided for each language type along with the computing models that recognize them, such as pushdown automata for context-free Type-2 languages.
This document discusses converting non-deterministic finite automata (NFA) to deterministic finite automata (DFA). NFAs can have multiple transitions with the same symbol or no transition for a symbol, while DFAs have a single transition for each symbol. The document provides examples of NFAs and their representations, and explains how to systematically construct a DFA that accepts the same language as a given NFA by considering all possible state combinations in the NFA. It also notes that NFAs and DFAs have equal expressive power despite their differences, and discusses minimizing DFAs and relationships to other automata models.
The document provides an introduction to automata theory and finite state automata (FSA). It defines an automaton as an abstract computing device or mathematical model used in computer science and computational linguistics. The reading discusses pioneers in automata theory like Alan Turing and his development of Turing machines. It then gives an overview of finite state automata, explaining concepts like states, transitions, alphabets, and using a example of building an FSA for a "sheeptalk" language to demonstrate these components.
This document provides an overview of Turing machines including:
- Turing machines are mathematical models that can perform any computation like a computer and have an infinite tape with a tape head.
- A Turing machine is defined by 7 tuples including states, alphabets, transition function, and blank symbols.
- Multitape Turing machines have multiple tapes that can be accessed independently by separate heads.
- The instantaneous description specifies the current state, tape symbol under the head, and full tape configuration.
- Transition diagrams visually represent the transition function that specifies how the tape and state change based on the current symbol.
Compiler Design LR parsing SLR ,LALR CLRRiazul Islam
The document introduces LR parsing and simple LR parsing. It discusses LR(k) parsing which scans input from left to right and constructs a rightmost derivation in reverse. It then focuses on simple LR parsing and describes parser states and items. Examples of parsing expressions are provided to illustrate closure computation. The document also discusses more powerful LR parsers that use lookahead and the canonical LR and LALR methods. It provides examples of LR(1) item sets and describes constructing an LALR parsing table.
This document provides an introduction to finite automata. It defines key concepts like alphabets, strings, languages, and finite state machines. It also describes the different types of automata, specifically deterministic finite automata (DFAs) and nondeterministic finite automata (NFAs). DFAs have a single transition between states for each input, while NFAs can have multiple transitions. NFAs are generally easier to construct than DFAs. The next class will focus on deterministic finite automata in more detail.
Decision properties of reular languagesSOMNATHMORE2
This document discusses decision properties of regular languages. It defines regular languages as those that can be described by regular expressions and accepted by finite automata. It explains that decision properties are algorithms that take a formal language description and determine properties like emptiness, finiteness, membership in the language, and equivalence to another language. The key decision properties - emptiness, finiteness, membership, and equivalence - are then defined along with the algorithms to determine each. Examples are provided to illustrate the algorithms. Applications of decision properties in areas like data validation and parsing are also mentioned.
This document summarizes key topics in intermediate code generation discussed in Chapter 6, including:
1) Variants of syntax trees like DAGs are introduced to share common subexpressions. Three-address code is also discussed where each instruction has at most three operands.
2) Type checking and type expressions are covered, along with translating expressions and statements to three-address code. Control flow statements like if/else are also translated using techniques like backpatching.
3) Backpatching allows symbolic labels in conditional jumps to be resolved by a later pass that inserts actual addresses, avoiding an extra pass. This and other control flow translation topics are covered.
This document discusses top-down parsing and different types of top-down parsers, including recursive descent parsers, predictive parsers, and LL(1) grammars. It explains how to build predictive parsers without recursion by using a parsing table constructed from the FIRST and FOLLOW sets of grammar symbols. The key steps are: 1) computing FIRST and FOLLOW, 2) filling the predictive parsing table based on FIRST/FOLLOW, 3) using the table to parse inputs in a non-recursive manner by maintaining the parser's own stack. An example is provided to illustrate constructing the FIRST/FOLLOW sets and parsing table for a sample grammar.
The document discusses compilers and their role in translating high-level programming languages into machine-readable code. It notes that compilers perform several key functions: lexical analysis, syntax analysis, generation of an intermediate representation, optimization of the intermediate code, and finally generation of assembly or machine code. The compiler allows programmers to write code in a high-level language that is easier for humans while still producing efficient low-level code that computers can execute.
This document defines context-free grammars (CFGs) and context-free languages (CFLs). A CFG is defined by a 4-tuple specifying variables, terminals, productions, and a start variable. Derivations in a CFG involve replacing variables according to productions. A language is context-free if some CFG generates it. Examples of CFGs that generate canonical CFLs like {anbn} are given. Parse trees illustrate derivations, and leftmost/rightmost derivations are defined. Ambiguous grammars that generate the same string in different ways are discussed.
The document discusses code generation in compilers. It describes the main tasks of the code generator as instruction selection, register allocation and assignment, and instruction ordering. It then discusses various issues in designing a code generator such as the input and output formats, memory management, different instruction selection and register allocation approaches, and choice of evaluation order. The target machine used is a hypothetical machine with general purpose registers, different addressing modes, and fixed instruction costs. Examples of instruction selection and utilization of addressing modes are provided.
This presentation discusses context-free grammars. It defines context-free grammars and provides an example. It also discusses parse trees, including how they are generated and different types (top-down and bottom-up). Examples are provided to demonstrate leftmost and rightmost derivations and parse trees. The document concludes that the grammar presented, with production rules of X → X+X | X*X |X| a, is ambiguous as there are two possible parse trees for the string "a+a*a".
1. A parse tree shows how the start symbol of a grammar derives a string in the language by using interior nodes labeled with nonterminals and children labeled with terminals or nonterminals according to the grammar's productions.
2. An ambiguous grammar is one where a single string can have more than one parse tree, leftmost derivation, rightmost derivation, or other derivation according to the grammar.
3. Operator precedence and associativity determine the order of operations when multiple operators are present in an expression. For example, multiplication generally has higher precedence than addition, and most operators associate left-to-right.
Linear bounded automata are a type of automaton that operates like a Turing machine but with a tape bounded by the length of the input string. They are more powerful than pushdown automata but less powerful than Turing machines. The computation is restricted to a constant bounded area between left and right end markers on the tape. Linear bounded automata accept context sensitive languages.
The document describes pushdown automata (PDA) which are analogous to context-free languages in the same way that finite automata are analogous to regular languages. A PDA has states, input symbols, stack symbols, transition functions, an initial state, initial stack symbol, and accepting states. The transition function specifies state transitions based on the current state, input symbol, and top of stack symbol and can modify the stack. The document provides examples of PDAs for languages of the form wwr and balanced parentheses and discusses how PDAs work by changing their instantaneous descriptions as the input is processed and stack is modified.
The document discusses issues in code generation by a compiler. It defines code generation as converting an intermediate representation into executable machine code. The code generator accesses symbol tables and performs multiple passes over intermediate forms. Key issues addressed include the input to the code generator, generating code for the target machine, memory management, instruction selection, register allocation, and optimization techniques like reordering independent instructions to improve efficiency.
This document summarizes a lecture on automata theory, specifically discussing non-regular languages, the pumping lemma, and regular expressions. It introduces the language B={0n1n | n ≥ 0} as a non-regular language that cannot be recognized by a DFA. It then proves the pumping lemma theorem and uses it to show that B and the language of strings with equal numbers of 0s and 1s are non-regular. Finally, it defines regular expressions as a way to describe languages and provides examples of regular expressions and their meanings.
The document discusses syntax analysis and parsing. It defines context-free grammars and different types of grammars. It also discusses derivation, parse trees, ambiguity in grammars and different parsing techniques like top-down and bottom-up parsing.
Finite Automata: Deterministic And Non-deterministic Finite Automaton (DFA)Mohammad Ilyas Malik
The term "Automata" is derived from the Greek word "αὐτόματα" which means "self-acting". An automaton (Automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically.
This document discusses Noam Chomsky's hierarchy of formal languages. It introduces Chomsky's classification of formal languages from Type-0 to Type-3 based on the type of grammar that generates them. Type-0 languages are the most powerful, being generated by unrestricted grammars and equivalent to Turing machines. Type-3 languages are the simplest, being generated by regular grammars and equivalent to finite state automata. Examples are provided for each language type along with the computing models that recognize them, such as pushdown automata for context-free Type-2 languages.
This document discusses converting non-deterministic finite automata (NFA) to deterministic finite automata (DFA). NFAs can have multiple transitions with the same symbol or no transition for a symbol, while DFAs have a single transition for each symbol. The document provides examples of NFAs and their representations, and explains how to systematically construct a DFA that accepts the same language as a given NFA by considering all possible state combinations in the NFA. It also notes that NFAs and DFAs have equal expressive power despite their differences, and discusses minimizing DFAs and relationships to other automata models.
The document provides an introduction to automata theory and finite state automata (FSA). It defines an automaton as an abstract computing device or mathematical model used in computer science and computational linguistics. The reading discusses pioneers in automata theory like Alan Turing and his development of Turing machines. It then gives an overview of finite state automata, explaining concepts like states, transitions, alphabets, and using a example of building an FSA for a "sheeptalk" language to demonstrate these components.
This document provides an overview of Turing machines including:
- Turing machines are mathematical models that can perform any computation like a computer and have an infinite tape with a tape head.
- A Turing machine is defined by 7 tuples including states, alphabets, transition function, and blank symbols.
- Multitape Turing machines have multiple tapes that can be accessed independently by separate heads.
- The instantaneous description specifies the current state, tape symbol under the head, and full tape configuration.
- Transition diagrams visually represent the transition function that specifies how the tape and state change based on the current symbol.
Compiler Design LR parsing SLR ,LALR CLRRiazul Islam
The document introduces LR parsing and simple LR parsing. It discusses LR(k) parsing which scans input from left to right and constructs a rightmost derivation in reverse. It then focuses on simple LR parsing and describes parser states and items. Examples of parsing expressions are provided to illustrate closure computation. The document also discusses more powerful LR parsers that use lookahead and the canonical LR and LALR methods. It provides examples of LR(1) item sets and describes constructing an LALR parsing table.
This document provides an introduction to finite automata. It defines key concepts like alphabets, strings, languages, and finite state machines. It also describes the different types of automata, specifically deterministic finite automata (DFAs) and nondeterministic finite automata (NFAs). DFAs have a single transition between states for each input, while NFAs can have multiple transitions. NFAs are generally easier to construct than DFAs. The next class will focus on deterministic finite automata in more detail.
Decision properties of reular languagesSOMNATHMORE2
This document discusses decision properties of regular languages. It defines regular languages as those that can be described by regular expressions and accepted by finite automata. It explains that decision properties are algorithms that take a formal language description and determine properties like emptiness, finiteness, membership in the language, and equivalence to another language. The key decision properties - emptiness, finiteness, membership, and equivalence - are then defined along with the algorithms to determine each. Examples are provided to illustrate the algorithms. Applications of decision properties in areas like data validation and parsing are also mentioned.
This document summarizes key topics in intermediate code generation discussed in Chapter 6, including:
1) Variants of syntax trees like DAGs are introduced to share common subexpressions. Three-address code is also discussed where each instruction has at most three operands.
2) Type checking and type expressions are covered, along with translating expressions and statements to three-address code. Control flow statements like if/else are also translated using techniques like backpatching.
3) Backpatching allows symbolic labels in conditional jumps to be resolved by a later pass that inserts actual addresses, avoiding an extra pass. This and other control flow translation topics are covered.
This document discusses top-down parsing and different types of top-down parsers, including recursive descent parsers, predictive parsers, and LL(1) grammars. It explains how to build predictive parsers without recursion by using a parsing table constructed from the FIRST and FOLLOW sets of grammar symbols. The key steps are: 1) computing FIRST and FOLLOW, 2) filling the predictive parsing table based on FIRST/FOLLOW, 3) using the table to parse inputs in a non-recursive manner by maintaining the parser's own stack. An example is provided to illustrate constructing the FIRST/FOLLOW sets and parsing table for a sample grammar.
The document discusses compilers and their role in translating high-level programming languages into machine-readable code. It notes that compilers perform several key functions: lexical analysis, syntax analysis, generation of an intermediate representation, optimization of the intermediate code, and finally generation of assembly or machine code. The compiler allows programmers to write code in a high-level language that is easier for humans while still producing efficient low-level code that computers can execute.
This document defines context-free grammars (CFGs) and context-free languages (CFLs). A CFG is defined by a 4-tuple specifying variables, terminals, productions, and a start variable. Derivations in a CFG involve replacing variables according to productions. A language is context-free if some CFG generates it. Examples of CFGs that generate canonical CFLs like {anbn} are given. Parse trees illustrate derivations, and leftmost/rightmost derivations are defined. Ambiguous grammars that generate the same string in different ways are discussed.
The document discusses code generation in compilers. It describes the main tasks of the code generator as instruction selection, register allocation and assignment, and instruction ordering. It then discusses various issues in designing a code generator such as the input and output formats, memory management, different instruction selection and register allocation approaches, and choice of evaluation order. The target machine used is a hypothetical machine with general purpose registers, different addressing modes, and fixed instruction costs. Examples of instruction selection and utilization of addressing modes are provided.
This presentation discusses context-free grammars. It defines context-free grammars and provides an example. It also discusses parse trees, including how they are generated and different types (top-down and bottom-up). Examples are provided to demonstrate leftmost and rightmost derivations and parse trees. The document concludes that the grammar presented, with production rules of X → X+X | X*X |X| a, is ambiguous as there are two possible parse trees for the string "a+a*a".
1. A parse tree shows how the start symbol of a grammar derives a string in the language by using interior nodes labeled with nonterminals and children labeled with terminals or nonterminals according to the grammar's productions.
2. An ambiguous grammar is one where a single string can have more than one parse tree, leftmost derivation, rightmost derivation, or other derivation according to the grammar.
3. Operator precedence and associativity determine the order of operations when multiple operators are present in an expression. For example, multiplication generally has higher precedence than addition, and most operators associate left-to-right.
Linear bounded automata are a type of automaton that operates like a Turing machine but with a tape bounded by the length of the input string. They are more powerful than pushdown automata but less powerful than Turing machines. The computation is restricted to a constant bounded area between left and right end markers on the tape. Linear bounded automata accept context sensitive languages.
The document describes pushdown automata (PDA) which are analogous to context-free languages in the same way that finite automata are analogous to regular languages. A PDA has states, input symbols, stack symbols, transition functions, an initial state, initial stack symbol, and accepting states. The transition function specifies state transitions based on the current state, input symbol, and top of stack symbol and can modify the stack. The document provides examples of PDAs for languages of the form wwr and balanced parentheses and discusses how PDAs work by changing their instantaneous descriptions as the input is processed and stack is modified.
The document discusses issues in code generation by a compiler. It defines code generation as converting an intermediate representation into executable machine code. The code generator accesses symbol tables and performs multiple passes over intermediate forms. Key issues addressed include the input to the code generator, generating code for the target machine, memory management, instruction selection, register allocation, and optimization techniques like reordering independent instructions to improve efficiency.
This document summarizes a lecture on automata theory, specifically discussing non-regular languages, the pumping lemma, and regular expressions. It introduces the language B={0n1n | n ≥ 0} as a non-regular language that cannot be recognized by a DFA. It then proves the pumping lemma theorem and uses it to show that B and the language of strings with equal numbers of 0s and 1s are non-regular. Finally, it defines regular expressions as a way to describe languages and provides examples of regular expressions and their meanings.
The document discusses syntax analysis and parsing. It defines context-free grammars and different types of grammars. It also discusses derivation, parse trees, ambiguity in grammars and different parsing techniques like top-down and bottom-up parsing.
The document discusses context free grammars and related concepts. It defines context free grammars and provides examples. It also discusses Chomsky hierarchy, classifying grammars into types 0-3 (unrestricted to regular) based on production rules. Formal languages generated by each grammar type are described along with their properties and closure properties. Context free grammars are defined in more detail, covering derivation, Backus-Naur form, and leftmost and rightmost derivations.
Context free grammars (CFGs) provide a formal way to describe the structure of languages by defining rewrite rules for replacing nonterminal symbols with strings of terminals and nonterminals. A CFG consists of variables, terminals, production rules, and a starting variable. Production rules take the form of replacing a single nonterminal with a string. CFGs can describe the recursive structure of natural languages but not agreement or reference. Examples are given for generating well-formed parentheses strings and showing how parse trees and derivations work. Ambiguous grammars that have multiple parse trees for some strings are discussed along with attempts to disambiguate grammars.
Automata theory - describes to derives string from Context free grammar - derivation and parse tree
normal forms - Chomsky normal form and Griebah normal form
This document introduces the key concepts in the theory of computation, including automata, formal languages, and grammars. It defines automata as abstract models that accept input, process it, and produce output. Formal languages are sets of strings formed from symbols according to rules, and grammars are sets of rules for generating the strings in a language. The document also reviews mathematical concepts needed to study computation and provides examples of operations on strings and languages.
This document discusses regular languages and finite automata. It begins by defining regular languages and expressions, and describing the equivalence between non-deterministic finite automata (NFAs) and deterministic finite automata (DFAs). It then discusses converting between regular expressions, NFAs with epsilon transitions, NFAs without epsilon transitions, and DFAs. The document provides examples of regular expressions and conversions between different representations. It concludes by describing the state elimination, formula, and Arden's methods for converting a DFA to a regular expression.
The document discusses context-free languages and pushdown automata. It defines context-free grammars and languages, and provides examples of grammars and the strings they generate. It also defines pushdown automata formally as a 6-tuple with states, input alphabet, stack alphabet, transition function, start state, and accept states. Pushdown automata are similar to finite automata but have an additional stack which allows them to recognize some non-regular languages.
LECTURE 1 ALPHABET,STRINGS, LANGUAGE CHOMSKY TYPES OF GRAMMAR.pptxAbhishekKumarPandit5
The document discusses topics related to formal languages and automata theory. It covers types of formal languages, alphabets and strings, finite automata including DFAs and NFDAs, grammars including regular, context-free and context-sensitive grammars. It also discusses regular expressions and their use to represent regular languages that can be accepted by finite automata. Specific examples of languages and production rules are provided.
Syntax defines the grammatical rules of a programming language. There are three levels of syntax: lexical, concrete, and abstract. Lexical syntax defines tokens like literals and identifiers. Concrete syntax defines the actual representation using tokens. Abstract syntax describes a program's information without implementation details. Backus-Naur Form (BNF) uses rewriting rules to specify a grammar. BNF grammars can be ambiguous. Extended BNF simplifies recursive rules. Syntax analysis transforms a program into an abstract syntax tree used for semantic analysis and code generation.
Introduction:
A context-free grammar (CFG) is a term used in formal languages theory to describe a certain type of formal grammar. A context-free grammar is a set of production rules that describe all possible strings in a given formal language. Production rules are simple replacements. For example, the rule
A α
This document summarizes Noam Chomsky's 1957 work defining the Chomsky hierarchy of formal languages. It introduces the four types of grammars - Type-3 (regular), Type-2 (context-free), Type-1 (context-sensitive), and Type-0 (recursively enumerable) - and describes their defining production rules. Context-free grammars, which generate context-free languages, are discussed in more detail. Examples are provided to illustrate context-free grammars and their ability to generate non-regular languages like {anbn}. Pushdown automata, which are equivalent to context-free grammars, are also introduced.
In automata theory, a deterministic pushdown automaton (DPDA or DPA) is a variation of the pushdown automaton. The DPDA accepts the deterministic context-free languages, a proper subset of context-free languages. Machine transitions are based on the current state and input symbol, and also the current topmost symbol of the stack. Symbols lower in the stack are not visible and have no immediate effect. Machine actions include pushing, popping, or replacing the stack top. A deterministic pushdown automaton has at most one legal transition for the same combination of input symbol, state, and top stack symbol. This is where it differs from the nondeterministic pushdown automaton.
The document summarizes key concepts about context-free grammars and parsing from the book "Compiler Construction: Principles and Practice" by Kenneth C. Louden. It covers notations like EBNF and syntax diagrams for representing grammars, properties of context-free languages, and provides grammar rules and diagrams for a sample TINY language as an example.
This document discusses automata theory and focuses on grammars, languages, and finite state machines. It defines key terminology like alphabets, strings, languages, and regular expressions. It explains Chomsky's hierarchy of formal languages from type-3 regular languages to type-0 recursively enumerable languages. The document also discusses finite state automata (FSA), deterministic finite automata (DFA), non-deterministic finite automata (NFA), context-free grammars, pushdown automata, and Turing machines. Examples of grammars, languages, and finite state machines are provided to illustrate these concepts.
Finite-state morphological parsing uses finite-state transducers to parse words into their morphological components like stems and affixes. It requires a lexicon of stems and affixes, morphotactic rules describing valid morpheme combinations, and orthographic rules for spelling changes. The parser is built as a cascade of finite-state automata representing the lexicon, morphotactics and spelling rules. It maps surface word forms onto their underlying lexical representations including stems and morphological features. This allows morphological analysis of both regular and irregular forms.
The document discusses syntax analysis and parsing. It covers context-free grammars, Backus-Naur Form (BNF), Extended BNF, and different parsing techniques like recursive descent parsing and LL parsing. It also discusses Scala's combinator parser, which uses parser combinators to parse input based on a grammar.
A195259101 22750 24_2018_grammars and languages generated by grammarsMohd Arif Ansari
This document discusses formal languages and natural language processing. It defines a formal language as a set of strings over a finite alphabet. Examples of operations on languages are provided, such as concatenation, intersection, union, and complement. Formal languages can be specified using grammars, regular expressions, automata, or decision problems. Four types of grammars are described, from unrestricted Type-0 grammars to regular Type-3 grammars. The relationship between grammars, languages, and machines is also overviewed.
The document discusses different types of data marts:
- Dependent data marts draw data directly from a centralized data warehouse, allowing for unified data access but with a focus on a specific group's needs.
- Independent data marts are standalone systems built from direct access to operational or external data sources without using a centralized warehouse. They are suitable for smaller groups.
- Hybrid data marts can integrate data from both a centralized warehouse and other sources, providing flexibility for ad hoc integration needs.
This document discusses the different statement interfaces in JDBC - Statement, PreparedStatement, and CallableStatement. It provides the following information:
- The Statement interface is used for general database access and static SQL. PreparedStatement accepts parameters and is useful for repeated SQL. CallableStatement accesses stored procedures and can use input, output, and input/output parameters.
- To create a statement, the Connection object's createStatement method is used. PreparedStatement is created with prepareStatement and CallableStatement with prepareCall.
- Parameters are represented by ? and bound using set methods. PreparedStatement and CallableStatement allow dynamic SQL.
- Statement methods like execute, executeQuery, executeUpdate work
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2. Context-Free Languages
•Context-Free Languages (CFL) are described
using Context-Free Grammars (CFG).
•A CFG is a simple recursive method of
specifying grammar rules which can generate
strings in a language – these languages are the
CFL’s.
3. Context-Free Grammars
• The following is an example of a CFG, call it G1:
• A → 1A0 (A and B = variables)
• A → B
• B → # (0, 1 and # = terminals)
• A grammar consists of a collection of substitution rules
(projections).
• A is start variable in this case – usually occurs on left
hand side of topmost rule.
4. Use grammar to describe a language by
generating each string of language:
• Write down start variable.
• Find a variable and a rule which starts with that variable. Replace
written variable with the right hand side of this rule.
• Repeat the second step until no variables remain.
5. •All strings generated in this manner constitute
the language of the grammar.
•L(G1) = language of grammar G1.
•Can show that L(G1) is {1n
#0n
| n ≥ 0}.
•Any language that can be generated by some
context-free grammar is called a context-free
language.
6. Defining CFG
• Informally a CFG consists of:
• A set of replacement rules, each having a Left-
Hand Side (LHS) and a Right-Hand Side (RHS).
• Two types of symbols; variables and terminals.
• LHS of each rule is a single variable (no
terminals).
• RHS of each rule is a string of zero or more
variables and terminals.
• A string consists of only terminals.
7. Definition of a CFG
•Formally, a context-free grammar is a 4-tuple
(V, T , R, S ), where
• V are the variables (finite set)
• T are the terminal states (finite set)
• R is the set of rules
• S is the start variable, S V
8. Context-Free Grammars
• In grammar G1, V = {A, B}, Σ = {0, 1, #}, S = A, and R
is the collections of the rules:
• A → 1A0
• A → B
• B → #
• Consider G3 = ({S}, {a,b}, R, S). The set of rules R, is
• S → aSb | SS | ε
• This grammar generates strings such as ab, abab,
aababb and aaabbb.
9. Pushdown Automata (PDA)
•Pushdown Automata are similar to
nondeterministic finite automata but have an
extra element – stack.
•This stack provided extra memory space.
•Also allows pushdown automata to recognise
some nonregular languages.
10. Context Free Language
•A language is context free if and only if some
pushdown automata recognises it.
•Every regular language is recognised by a
finite automaton and every finite automaton
is automatically a pushdown automaton that
ignores the stack, we can note that every
regular language is also a context-free
language.
12. Closure Properties of
CFL
The context free languages are closed under
the following operations:
1.Union
2.Concatenation
3.Closure
4.Homomorphism
13. Derivation Tree
Definition: Let G = (V, T, P, S) be a CFG. A tree is a
derivation (or parse) tree if:
• Every vertex has a label from V union T union {ε}
• The label of the root is S
• If a vertex with label A has children with labels X1, X2,
…, Xn, from left to right, then
A –> X1, X2,…, Xn must be a production in P
• If a vertex has label ε, then that vertex is a leaf and
the only child of its’ parent
More Generally, a derivation tree can be defined with
any non-terminal as the root.
14.
15. Backus-Naur Form
• The backus-naur form is a convenient notation use
to represent CFG in an intuitive and more compact
manner.
• In BNF we use the following symbols:
< > := |
• Given a CFG (V, T , R, S ) a variable is enclosed in
< and >.A terminal is represented as itself and a
production is represented as
<V>:=symbols
16. •When describing languages,BNF is a formal
notation for encoding grammars.
•Many programming languages,protocols or
formats have a BNF description in their
specification.
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