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We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLfMT), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring…

Bit-vector formulas arising from hardware verification problems often contain word-level arithmetic operations. Empirical evidence shows that state-of-the-art SMT solvers are not very efficient at reasoning about bit-vector formulas with…

Bit-vectors, which are integers in a finite number of bits, are ubiquitous in software and hardware systems. In this work, we consider the satisfiability modulo theories (SMT) of bit-vectors. Unlike normal integers, the arithmetics of…

The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning,…

Many practical problems are characterized by a preference relation over admissible solutions, where preferred solutions are minimal in some sense. For example, a preferred diagnosis usually comprises a minimal set of reasons that is…

Large language models (LLMs) are increasingly explored for NP-hard combinatorial optimization problems, but most existing methods emphasize feasible-instance solution generation and do not explicitly address infeasibility detection. We…

While large language models (LLMs) have demonstrated remarkable success on a broad range of tasks, math reasoning remains a challenging one. One of the approaches for improving math reasoning is self-correction, which designs self-improving…

Large language models (LLMs) have shown impressive performance on reasoning benchmarks like math and logic. While many works have largely assumed well-defined tasks, real-world queries are often underspecified and only solvable by acquiring…

We introduce SLR, an end-to-end framework for systematic evaluation and training of Large Language Models (LLMs) via Scalable Logical Reasoning. Given a user's task specification, SLR automatically synthesizes (i) an instruction prompt for…

Inductive Logic Programming (ILP) provides interpretable rule learning in relational domains, yet remains limited in its ability to induce and reason with numerical constraints. Classical ILP systems operate over discrete predicates and…

Propositional model counting} (#SAT), i.e., counting the number of satisfying assignments of a propositional formula, is a problem of significant theoretical and practical interest. Due to the inherent complexity of the problem, approximate…

In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…

As Large Language Models (LLMs) increasingly assist secure software development, their ability to meet the rigorous demands of Rust program verification remains unclear. Existing evaluations treat Rust verification as a black box, assessing…

Large Reasoning Models (LRMs) have revolutionized complex problem-solving, yet they exhibit a pervasive "overthinking", generating unnecessarily long reasoning chains. While current solutions improve token efficiency, they often sacrifice…

The Model Constructing Satisfiability (MCSat) approach to the SMT problem extends the ideas of CDCL from the SAT level to the theory level. Like SAT, its search is driven by incrementally constructing a model by assigning concrete values to…

When solving combinatorial problems, pruning symmetric solution candidates from the search space is essential. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints…

The NeuroSAT neural network architecture was recently introduced for predicting properties of propositional formulae. When trained to predict the satisfiability of toy problems, it was shown to find solutions and unsatisfiable cores on its…

Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…

We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…

Recent supervised fine-tuning (SFT) approaches have significantly improved language models' performance on mathematical reasoning tasks, even when models are trained at a small scale. However, the specific capabilities enhanced through such…