Related papers: The nature of loops in programming

Software verification has emerged as a key concern for ensuring the continued progress of information technology. Full verification generally requires, as a crucial step, equipping each loop with a "loop invariant". Beyond their role in…

Invariants are the predominant approach to verify the correctness of loops. As an alternative, loop contracts, which make explicit the premise and conclusion of the underlying induction proof, can sometimes capture correctness conditions…

Loop invariants are software properties that hold before and after every iteration of a loop. As such, invariants provide inductive arguments that are key in automating the verification of program loops. The problem of generating loop…

Loop invariants play a central role in the verification of imperative programs. However, finding these invariants is often a difficult and time-consuming task for the programmer. We have previously shown how program transformation can be…

We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…

Great advances in program analysis would be enabled if it were possible to derive the function of a program from inputs to outputs (or from initial states to final states, depending on how we model program semantics). Efforts to do so have…

A well-established approach to reasoning about loops during program analysis is to capture the effect of a loop by extracting recurrences from the loop; these express relationships between the values of variables, or program properties such…

Invariants are key to formal loop verification as they capture loop properties that are valid before and after each loop iteration. Yet, generating invariants is a notorious task already for syntactically restricted classes of loops. Rather…

One of the obstacles in automatic program proving is to obtain suitable loop invariants. The invariant of a loop is a weakened form of its postcondition (the loop's goal, also known as its contract); the present work takes advantage of this…

A program invariant is a property that holds for every execution of the program. Recent work suggest to infer likely-only invariants, via dynamic analysis. A likely invariant is a property that holds for some executions but is not…

Provably correct software is one of the key challenges in our softwaredriven society. While formal verification establishes the correctness of a given program, the result of program synthesis is a program which is correct by construction.…

We present the first approach to prove non-termination of integer programs that is based on loop acceleration. If our technique cannot show non-termination of a loop, it tries to accelerate it instead in order to find paths to other…

Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to…

Looping is one of the fundamental logical instructions used for repeating a block of code. It is used in programs across all programming languages. Traditionally, in languages like C, the for loop is used extensively for repeated execution…

Provably correct software is one of the key challenges of our software-driven society. Program synthesis -- the task of constructing a program satisfying a given specification -- is one strategy for achieving this. The result of this task…

In considering the reliability of numerical programs, it is normal to "limit our study to the semantics dealing with numerical precision" (Martel, 2005). On the other hand, there is a great deal of work on the reliability of programs that…

A simple linear loop is a simple while loop with linear assignments and linear loop guards. If a simple linear loop has only two program variables, we give a complete algorithm for computing the set of all the inputs on which the loop does…

Techniques to achieve various forms of test coverage, such as branch coverage, typically do not iterate loops; in other words, they treat a loop as a conditional, executed zero or one time. Existing work by the author and collaborators…

Loop invariants are properties of a program loop that hold both before and after each iteration of the loop. They are often used to verify programs and ensure that algorithms consistently produce correct results during execution.…

In this paper, we define two particular forms of non-termination, namely loops and binary chains, in an abstract framework that encompasses term rewriting and logic programming. The definition of loops relies on the notion of compatibility…