Related papers: Invariant Relations: A Bridge from Programs to Equ…

In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…

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…

We introduce a relational approach to program synthesis. The key idea is to decompose synthesis tasks into simpler relational synthesis subtasks. Specifically, our representation decomposes a training input-output example into sets of input…

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…

This paper presents a program analysis method that generates program summaries involving polynomial arithmetic. Our approach builds on prior techniques that use solvable polynomial maps for summarizing loops. These techniques are able to…

This paper presents a new method for automatically generating numerical invariants for imperative programs. Given a program, our procedure computes a binary input/output relation on program states which over-approximates the behaviour of…

Loop invariants play a very important role in proving correctness of programs. In this paper, we address the problem of generating invariants of polynomial loop programs. We present a new approach, for generating polynomial equation…

We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its…

This article focuses on automatically generating polynomial equations that are inductive loop invariants of computer programs. We propose a new algorithm for this task, which is based on polynomial interpolation. Though the proposed…

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…

The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…

Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…

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.…

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…

Human written source code in imperative programming languages exhibits typical patterns for variable use such as flags, loop iterators, counters, indices, bitvectors etc. Although it is widely understood by practitioners that these variable…

In this article, we discuss a flow--sensitive analysis of equality relationships for imperative programs. We describe its semantic domains, general purpose operations over abstract computational states (term evaluation and identification,…

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…

We present an algorithm for synthesizing program loops satisfying a given polynomial loop invariant. The class of loops we consider can be modeled by a system of algebraic recurrence equations with constant coefficients. We turn the task of…

In Programming by Example, a system attempts to infer a program from input and output examples, generally by searching for a composition of certain base functions. Performing a naive brute force search is infeasible for even mildly involved…

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…