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We introduce novel methods for encoding acyclicity and s-t-reachability constraints for propositional formulas with underlying directed graphs. They are based on vertex elimination graphs, which makes them suitable for cases where the…

We present a new approach to enhancing Answer Set Programming (ASP) with Constraint Processing techniques which allows for solving interesting Constraint Satisfaction Problems in ASP. We show how constraints on finite domains can be…

On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively…

Linear integer constraints are one of the most important constraints in combinatorial problems since they are commonly found in many practical applications. Typically, encodings to Boolean satisfiability (SAT) format of conjunctive normal…

Satisfiability of boolean formulae (SAT) has been a topic of research in logic and computer science for a long time. In this paper we are interested in understanding the structure of satisfiable and unsatisfiable sentences. In previous work…

Constraint Satisfaction Problem (CSP) is a framework for modeling and solving a variety of real-world problems. Once the problem is expressed as a finite set of constraints, the goal is to find the variables' values satisfying them. Even…

Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…

In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.

The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…

Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…

Code optimization and high level synthesis can be posed as constraint satisfaction and optimization problems, such as graph coloring used in register allocation. Graph coloring is also used to model more traditional CSPs relevant to AI,…

Symmetries are intrinsic to many combinatorial problems including Boolean Satisfiability (SAT) and Constraint Programming (CP). In SAT, the identification of symmetry breaking predicates (SBPs) is a well-known, often effective, technique…

In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists…

Picat is a logic-based, multi-paradigm programming language that integrates features from logic, functional, constraint, and imperative programming paradigms. This paper presents solutions to several problems from the 2024 Advent of Code…

Answer Set Programming (ASP) is a problem modeling and solving framework for several problems in KR with growing industrial applications. Also for studies of computational complexity and deeper insights into the hardness and its sources,…

A new stream of research was born in the last decade with the goal of mining itemsets of interest using Constraint Programming (CP). This has promoted a natural way to combine complex constraints in a highly flexible manner. Although CP…

The Circuit Satisfiability (CSAT) problem, a variant of the Boolean Satisfiability (SAT) problem, plays a critical role in integrated circuit design and verification. However, existing SAT solvers, optimized for Conjunctive Normal Form…

A core challenge in program synthesis is taming the large space of possible programs. Since program synthesis is essentially a combinatorial search, the community has sought to leverage powerful combinatorial constraint solvers. Here,…

Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin…

We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…