Related papers: What's Decidable about Syntax-Guided Synthesis?
The study of word equations (or the existential theory of equations over free monoids) is a central topic in mathematics and theoretical computer science. The problem of deciding whether a given word equation has a solution was shown to be…
System design automation aims to manage the design of embedded systems with ever-increasing complexity. To the success of system design automation, there is still a lack of systematic and formal design process because an entire design…
Multi-modal program synthesis refers to the task of synthesizing programs (code) from their specification given in different forms, such as a combination of natural language and examples. Examples provide a precise but incomplete…
The standard approach to logic in the literature in philosophy and mathematics, which has also been adopted in computer science, is to define a language (the syntax), an appropriate class of models together with an interpretation of…
Finite-state controllers (FSCs), such as plans with loops, are powerful and compact representations of action selection widely used in robotics, video games and logistics. There has been steady progress on synthesizing FSCs in deterministic…
Many data extraction tasks of practical relevance require not only syntactic pattern matching but also semantic reasoning about the content of the underlying text. While regular expressions are very well suited for tasks that require only…
We consider the problem of synthesizing a program given a probabilistic specification of its desired behavior. Specifically, we study the recent paradigm of distribution-guided inductive synthesis (DIGITS), which iteratively calls a…
We analyse the complexity of the satisfiability problem ssmSAT for State Space Models (SSM), which asks whether an input sequence can lead the model to an accepting configuration. We find that ssmSAT is undecidable in general, reflecting…
Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose…
Analytical solutions to differential equations offer exact, interpretable insight but are rarely available because discovering them requires expert intuition or exhaustive search of combinatorial spaces. We introduce SIGS, a neuro-symbolic…
Querying over disjunctive ASP with functions is a highly undecidable task in general. In this paper we focus on disjunctive logic programs with stratified negation and functions under the stable model semantics (ASP^{fs}). We show that…
We present a new domain-agnostic synthesis technique for generating programs from input-output examples. Our method, called metric program synthesis, relaxes the well-known observational equivalence idea (used widely in bottom-up…
In this paper, we investigate the problem of synthesizing computable functions of infinite words over an infinite alphabet (data $\omega$-words). The notion of computability is defined through Turing machines with infinite inputs which can…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
We discuss proving correctness and completeness of definite clause logic programs. We propose a method for proving completeness, while for proving correctness we employ a method which should be well known but is often neglected. Also, we…
The discovery of functional molecules is an expensive and time-consuming process, exemplified by the rising costs of small molecule therapeutic discovery. One class of techniques of growing interest for early-stage drug discovery is de novo…
Question Generation (QG) is fundamentally a simple syntactic transformation; however, many aspects of semantics influence what questions are good to form. We implement this observation by developing SynQG, a set of transparent syntactic…
Joint logical-numerical reasoning remains a major challenge for language models, yet existing datasets rely on fixed rule sets and offer limited control over task complexity, constraining their generalizability for evaluation and training.…
The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very…
Almost every programming language's syntax includes a notion of binder and corresponding bound occurrences, along with the accompanying notions of $\alpha$-equivalence, capture-avoiding substitution, typing contexts, runtime environments,…