Related papers: Inferring Loop Invariants using Postconditions

Infinite-state systems such as distributed protocols are challenging to verify using interactive theorem provers or automatic verification tools. Of these techniques, deductive verification is highly expressive but requires the user to…

We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…

We study causal inference in a multi-environment setting, in which the functional relations for producing the variables from their direct causes remain the same across environments, while the distribution of exogenous noises may vary. We…

Automated program verification often proceeds by exhibiting inductive invariants entailing the desired properties.For numerical properties, a classical class of invariants is convex polyhedra: solution sets of system of linear…

We present a variant of the quantum relational Hoare logic from (Unruh, POPL 2019) that allows us to use "expectations" in pre- and postconditions. That is, when reasoning about pairs of programs, our logic allows us to quantitatively…

Ensuring software correctness remains a fundamental challenge in formal program verification. One promising approach relies on finding polynomial invariants for loops. Polynomial invariants are properties of a program loop that hold before…

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…

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…

We study the complexity of invariant inference and its connections to exact concept learning. We define a condition on invariants and their geometry, called the fence condition, which permits applying theoretical results from exact concept…

We present in this paper a new technique for generating polynomial invariants, divided in two independent parts : a procedure that reduces polynomial assignments composed loops analysis to linear loops under certain hypotheses and a…

Automatically generating invariants, key to computer-aided analysis of probabilistic and deterministic programs and compiler optimisation, is a challenging open problem. Whilst the problem is in general undecidable, the goal is settled for…

We introduce the notion of porous invariants for multipath (or branching/nondeterministic) affine loops over the integers; these invariants are not necessarily convex, and can in fact contain infinitely many 'holes'. Nevertheless, we show…

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…

While there are many approaches for automatically proving termination of term rewrite systems, up to now there exist only few techniques to disprove their termination automatically. Almost all of these techniques try to find loops, where…

Human reasoning involves recognising common underlying principles across many examples. The by-products of such reasoning are invariants that capture patterns such as "if someone went somewhere then they are there", expressed using…

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 address the predicate generation problem in the context of loop invariant inference. Motivated by the interpolation-based abstraction refinement technique, we apply the interpolation theorem to synthesize predicates implicitly implied by…

We propose a new approach to automated theorem proving where an AlphaZero-style agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to…

Proof by coupling is a classical technique for proving properties about pairs of randomized algorithms by carefully relating (or coupling) two probabilistic executions. In this paper, we show how to automatically construct such proofs for…

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…