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In the Constraint Satisfaction Problem (CSP for short) the goal is to decide the existence of a homomorphism from a given relational structure $G$ to a given relational structure $H$. If the structure $H$ is fixed and $G$ is the only input,…
Generative AI agents are often expected to respond to complex user requests that have No One Right Answer (NORA), e.g., "design a vegetarian meal plan below 1800 calories". Such requests may entail a set of constraints that the agent should…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…
As large language models are increasingly used in high-stakes domains, it is essential that their outputs reflect not average} human preference, rather range of varying perspectives. Achieving such pluralism, however, remains challenging.…
Promise CSPs are a relaxation of constraint satisfaction problems where the goal is to find an assignment satisfying a relaxed version of the constraints. Several well-known problems can be cast as promise CSPs including approximate graph…
We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…
To appear in Theory and Practice of Logic Programming (TPLP) Bound Founded Answer Set Programming (BFASP) is an extension of Answer Set Programming (ASP) that extends stable model semantics to numeric variables. While the theory of BFASP is…
Many fundamental problems in artificial intelligence, knowledge representation, and verification involve reasoning about sets and relations between sets and can be modeled as set constraint satisfaction problems (set CSPs). Such problems…
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.…
While large language models (LLMs), such as GPT-3, appear to be robust and general, their reasoning ability is not at a level to compete with the best models trained for specific natural language reasoning problems. In this study, we…
Constraint Satisfaction Problems (CSPs, for short) make up a class of problems with applications in many areas of computer science. The first classification of these problems was given by Schaeffer who showed that every CSP over the domain…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
This work introduces (1) a technique that allows large language models (LLMs) to leverage user-provided code when solving programming tasks and (2) a method to iteratively generate modular sub-functions that can aid future code generation…
We study a model of constraint satisfaction problems geared towards instances with few variables but with domain of unbounded size (udCSP). Our model is inspired by recent work on FPT algorithms for MinCSP where frequently both upper and…
The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic…
This work is devoted to constraint solving motivated by the debugging of constraint logic programs a la GNU-Prolog. The paper focuses only on the constraints. In this framework, constraint solving amounts to domain reduction. A computation…
We extend the notion of a strong backdoor from the CSP setting to the Valued CSP setting (VCSP, for short). This provides a means for augmenting a class of tractable VCSP instances to instances that are outside the class but of small…
We present a method for verifying partial correctness properties of imperative programs that manipulate integers and arrays by using techniques based on the transformation of constraint logic programs (CLP). We use CLP as a metalanguage for…
Motivated by the progress made by large language models (LLMs), we introduce the framework of verbalized machine learning (VML). In contrast to conventional machine learning (ML) models that are typically optimized over a continuous…