Related papers: Formula Slicing: Inductive Invariants from Precond…
Loop invariant generation remains a critical bottleneck in automated program verification. Recent work has begun to explore the use of Large Language Models (LLMs) in this area, yet these approaches tend to lack a reliable and structured…
This paper proposes new derivations of three well-known sorting algorithms, in their functional formulation. The approach we use is based on three main ingredients: first, the algorithms are derived from a simpler algorithm, i.e. the…
Auto-active program verification rests on the ability to effectively the translation from annotated programs into verification conditions that are then discharged by automated theorem provers in the background. Characteristic such tools,…
Given a value computed within a program, an idempotent backward slice with respect to this value is a maximal subprogram that computes it. An informal notion of an idempotent slice has previously been used by Guimaraes et al. to transform…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
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.…
Fully automated verification of concurrent programs is a difficult problem, primarily because of state explosion: the exponential growth of a program state space with the number of its concurrently active components. It is natural to apply…
Morgan and McIver's weakest pre-expectation framework is one of the most well-established methods for deductive verification of probabilistic programs. Roughly, the idea is to generalize binary state assertions to real-valued expectations,…
Program slicing provides explanations that illustrate how program outputs were produced from inputs. We build on an approach introduced in prior work by Perera et al., where dynamic slicing was defined for pure higher-order functional…
Program slicing reduces a program to a smaller version that retains a chosen computation, referred to as a slicing criterion. One recent multi-lingual slicing approach, observation-based slicing (ORBS), speculatively deletes parts of the…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Deep learning has become the state-of-art tool in many applications, but the evaluation and training of deep models can be time-consuming and computationally expensive. The conditional computation approach has been proposed to tackle this…
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.…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in…
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…
Splitting a logic program allows us to reduce the task of computing its stable models to similar tasks for its subprograms. This can be used to increase solving performance and prove program correctness. We generalize the conditions under…
We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number…
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…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…