Related papers: What's Decidable about Syntax-Guided Synthesis?

Working with the simple types over a base type of natural numbers (including product types), we consider the question of when a type $\sigma$ is encodable as a definable retract of $\tau$: that is, when there are $\lambda$-terms…

Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper,…

We study the problem of synthesizing domain-specific languages (DSLs) for few-shot learning in symbolic domains. Given a base language and instances of few-shot learning problems, where each instance is split into training and testing…

Logic synthesis is a fundamental step in hardware design whose goal is to find structural representations of Boolean functions while minimizing delay and area. If the function is completely-specified, the implementation accurately…

Program correctness (in imperative and functional programming) splits in logic programming into correctness and completeness. Completeness means that a program produces all the answers required by its specification. Little work has been…

We describe a semidefinite programming framework for proving upper bounds on concrete sifting problems, and show that the Large Sieve can be interpreted as a special case of this framework. With a small tweak, the Larger Sieve also falls…

In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…

Formal languages let us define the textual representation of data with precision. Formal grammars, typically in the form of BNF-like productions, describe the language syntax, which is then annotated for syntax-directed translation and…

We describe techniques for synthesis and verification of recursive functional programs over unbounded domains. Our techniques build on top of an algorithm for satisfiability modulo recursive functions, a framework for deductive synthesis,…

Grammatical Error Correction (GEC) is a task of detecting and correcting grammatical errors in sentences. Recently, neural machine translation systems have become popular approaches for this task. However, these methods lack the use of…

Program synthesis is a class of regression problems where one seeks a solution, in the form of a source-code program, mapping the inputs to their corresponding outputs exactly. Due to its precise and combinatorial nature, program synthesis…

This research introduces a new parsing approach, based on earlier syntactic work on context free grammar (CFG) and generalized phrase structure grammar (GPSG). The approach comprises both a new parsing algorithm and a set of syntactic rules…

We target the problem of automatically synthesizing proofs of semantic equivalence between two programs made of sequences of statements. We represent programs using abstract syntax trees (AST), where a given set of semantics-preserving…

We study the fluted fragment of first-order logic which is often viewed as a multi-variable non-guarded extension to various systems of description logics lacking role-inverses. In this paper we show that satisfiable fluted sentences (even…

Metric Temporal Logic, $\mtlfull$ is amongst the most studied real-time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of time interval…

Mathematical reasoning remains challenging for LLMs due to complex logic and the need for precise computation. Existing methods enhance LLM reasoning by synthesizing datasets through problem rephrasing, but face issues with generation…

The satisfiability problem for SPARQL patterns is undecidable in general, since the expressive power of SPARQL 1.0 is comparable with that of the relational algebra. The goal of this paper is to delineate the boundary of decidability of…

Language models often achieve higher accuracy when reasoning step-by-step in complex tasks. However, even when arriving at a correct final answer, their rationales are often logically unsound or inconsistent. This is a major issue when…

Advances in logic programming and increasing industrial uptake of Datalog-inspired approaches demonstrate the emerging need to express powerful code analyses more easily. Declarative program analysis frameworks (e.g., using logic…

In recent years, there has been an increased interest in tools that establish \emph{incorrectness} rather than correctness of program properties. In this work we build on this approach by developing a novel methodology to prove…