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We present a compositional SMT-based algorithm for safety of procedural C programs that takes the heap into consideration as well. Existing SMT-based approaches are either largely restricted to handling linear arithmetic operations and…
We investigate the Constraint Satisfaction Problem (CSP) over templates with a group structure, and algorithms solving CSP that are equivariant, i.e. invariant under a natural group action induced by a template. Our main result is a method…
C-RASP is a simple programming language that was recently shown to capture concepts expressible by transformers. In this paper, we develop new algorithmic techniques for automatically verifying C-RASPs. To this end, we establish a…
Constraint satisfaction problems (CSPs) are an important formal framework for the uniform treatment of various prominent AI tasks, e.g., coloring or scheduling problems. Solving CSPs is, in general, known to be NP-complete and…
The CLP scheme uses Horn clauses and SLD resolution to generate multiple constraint satisfaction problems (CSPs). The possible CSPs include rational trees (giving Prolog) and numerical algorithms for solving linear equations and linear…
Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by…
Answer Set Programming (ASP) is a powerful declarative programming paradigm commonly used for solving challenging search and optimization problems. The modeling languages of ASP are supported by sophisticated solving algorithms (solvers)…
Large language models (LLMs) have demonstrated remarkable capabilities across diverse tasks. However, the truthfulness of their outputs is not guaranteed, and their tendency toward overconfidence further limits reliability. Uncertainty…
It is imperative to ensure the stability of every prediction made by a language model; that is, a language's prediction should remain consistent despite minor input variations, like word substitutions. In this paper, we investigate the…
We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a…
The Chinese Remainder Theorem for the integers says that every system of congruence equations is solvable as long as the system satisfies an obvious necessary condition. This statement can be generalized in a natural way to arbitrary…
We develop the novel machinery of smooth approximations, and apply it to confirm the CSP dichotomy conjecture for first-order reducts of the random tournament, various homogeneous graphs including the random graph, and for expansions of the…
The Verified Software Toolchain (VST) is a system for proving correctness of C programs using separation logic. By connecting to the verified compiler CompCert, it produces the strongest possible guarantees of correctness for real C code…
The fixed-template constraint satisfaction problem (CSP) can be seen as the problem of deciding whether a given primitive positive first-order sentence is true in a fixed structure (also called model). We study a class of problems that…
The CSP (constraint satisfaction problems) is a class of problems deciding whether there exists a homomorphism from an instance relational structure to a target one. The CSP dichotomy is a profound result recently proved by Zhuk (2020, J.…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
It is an open question whether the search and decision versions of promise CSPs are equivalent. Most known algorithms for PCSPs solve only their \emph{decision} variant, and it is unknown whether they can be adapted to solve \emph{search}…
This paper studies how to verify the conformity of a program with its specification and proposes a novel constraint-programming framework for bounded program verification (CPBPV). The CPBPV framework uses constraint stores to represent the…
Attempts to render deep learning models interpretable, data-efficient, and robust have seen some success through hybridisation with rule-based systems, for example, in Neural Theorem Provers (NTPs). These neuro-symbolic models can induce…
The determination of the number of mixture components (the order) of a finite mixture model has been an enduring problem in statistical inference. We prove that the closed testing principle leads to a sequential testing procedure (STP) that…