Related papers: Putting the Squeeze on Array Programs: Loop Verifi…

We describe a system to prove properties of programs. The key feature of this approach is a method to automatically synthesize inductive invariants of the loops contained in the program. The method is generic, i.e., it applies to a large…

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…

Static verification techniques leverage Boolean formula satisfiability solvers such as SAT and SMT solvers that operate on conjunctive normal form and first order logic formulae, respectively, to validate programs. They force bounds on…

Control barrier functions are a popular method of ensuring system safety, and these functions can be used to enforce invariance of a set under the dynamics of a system. A control barrier function must have certain properties, and one must…

How can we discern whether the covariance operator of a stochastic process is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for…

Answer set programming (ASP) and planning are two widely used paradigms for solving logic programs with declarative programming. In both cases, the quality of the input programs has a major influence on the quality and performance of the…

We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…

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 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…

Despite the tremendous advances that have been made in the last decade on developing useful machine-learning applications, their wider adoption has been hindered by the lack of strong assurance guarantees that can be made about their…

Automated software verification is a very active field of research which has made enormous progress both in theoretical and practical aspects. Recently, an important amount of research effort has been put into applying these techniques on…

We provide full certifications of two versions of merge sort of arrays in the verification-aware programming language Dafny. We start by considering schemas for applying the divide-and-conquer or partition method of solution to…

The problem of checking whether two programs are semantically equivalent or not has a diverse range of applications, and is consequently of substantial importance. There are several techniques that address this problem, chiefly by…

Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…

We present a new inductive rule for verifying lower bounds on expected values of random variables after execution of probabilistic loops as well as on their expected runtimes. Our rule is simple in the sense that loop body semantics need to…

Program reductions are used widely to simplify reasoning about the correctness of concurrent and distributed programs. In this paper, we propose a general approach to proof simplification of concurrent programs based on exploring generic…

Loop under-approximation is a technique that enriches C programs with additional branches that represent the effect of a (limited) range of loop iterations. While this technique can speed up the detection of bugs significantly, it…

Bounded Model Checking is one the most successful techniques for finding bugs in program. However, for programs with loops iterating over large-sized arrays, bounded model checkers often exceed the limit of resources available to them. We…

We present a proof by induction algorithm, which combines k-induction with invariants to model check embedded C software with bounded and unbounded loops. The k-induction algorithm consists of three cases: in the base case, we aim to find a…

Analyzing and verifying heap-manipulating programs automatically is challenging. A key for fighting the complexity is to develop compositional methods. For instance, many existing verifiers for heap-manipulating programs require…