Formal verification

FORMAL VERIFICATION
BY
C.RAJESWARI
II MSC IT
NADAR SARASWATHI COLLEGE OF ARTS AND SCIENCE
THENI.

INTRODUCTION
• Formal verification involves the use of rigorous, mathematical
techniques to demonstrate that computer programs have certain
desired properties.
• The methods of input-output assertions, weakest preconditions,
and structural induction are three commonly used techniques.

INPUT-OUTPUT ASSERTIONS
• The method of input-output assertions was introduced by Floyed (FLO67) and
refined by Hoare (HOA73) and Dijkstra (DIJ76). Floyd’s work was seminal to
the entire field of formal verification.
• Using input-output assertions, predicates are associated with the entry point,
the exist point, and various intermediate points in the source code.
• The notation (P) S (R) is used to mean that if predicate P is true prior to
executing code segment S, predicate R will be true following of S.
(1<i<N)i:=i+1(2<i<N+1)

CONTINUE….
• The minimal requirement is that a predicate be associated with each
innermost nested loop.
• Loop predicates must be shown to be invariant relations. A loop invariant
must be true independent of the number of loop traversed.in particular a
loop invariant must satisfy the following conditions:
1. It must be true on loop entry.
2. It must be true independent of the number of loop traversals.
3. It must imply the desired condition on loop exit.

WEAKEST PRECONDITIONS
• To be true independent of the number of loop traversals by the method of
weakest preconditions.
• Given a proposition of the from (P) S (R), P is the weakest precondition for S if
it is the weakest condition that will guarantee the truth of R following
execution of S.
• The weakest precondition is expressed as
P = wp(S,R)

CONTINUE….
• In practice P is found by working backwards from R.
• If S is an assignment statement of the form X:=E, the weakest precondition P
is obtained by substituting expression E in place of X everywhere X appears in
predicate R:
Wp(X:=E,R)=R(E X)
• For example:
Wp(A:=B+3, A=5)=(A=5 with B+3A)
=(B+3=5) or (B=2)

STRUCTURAL INDUCTION
• Structural induction us a formal verification technique based on the general
principle of mathematical induction.
• The induction must be performed on a partially ordered set that is well
founded (LEV80).
• Given set S having the necessary properties and a proposition P to be proved.

CONTINUE….
• Mathematical indication proceeds as follows:
1. Show P to be true for the minimal elements in S.
2. Assume P to be true for each element in S that has an ordinal
number less than or equal to N and show P to be true for the N + first
element in S.
• The set of natural numbers under the ordering ”<“ is a commonly used
induction set, and many properties of the natural numbers can be proved by
induction.

Formal verification

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Formal verification