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Over the last few decades, many distinct lines of research aimed at automating mathematics have been developed, including computer algebra systems (CASs) for mathematical modelling, automated theorem provers for first-order logic, SAT/SMT…

Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and…

Large language models (LLMs) now solve multi-step problems by emitting extended chains of thought. During the process, they often re-derive the same intermediate steps across problems, inflating token usage and latency. This saturation of…

Chain-of-thought (CoT) rationale enables language models to use additional task-related text for problem-solving, benefiting not only from detailed reasoning steps but also from the expanded computational space of longer inputs. Prior work…

Restart policy is an important technique used in modern Conflict-Driven Clause Learning (CDCL) solvers, wherein some parts of the solver state are erased at certain intervals during the run of the solver. In most solvers, variable…

Current inference scaling methods, such as Self-consistency and Best-of-N, have proven effective in improving the accuracy of LLMs on complex reasoning tasks. However, these methods rely heavily on the quality of candidate responses and are…

Many modern solvers and program analyzers rely on non-monotone reasoning (e.g. negation-as-failure, speculative updates, backtracking) for which classical monotone fixed-point methods do not apply. The general problem of finding the fixed…

Data analytic applications built upon big data processing frameworks such as Apache Spark are an important class of applications. Many of these applications are not latency-sensitive and thus can run as batch jobs in data centers. By…

In this paper, a new technique for the optimization of (partially) bound queries over disjunctive Datalog programs with stratified negation is presented. The technique exploits the propagation of query bindings and extends the Magic Set…

Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5…

Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically,…

\textbf{RE}trieval-\textbf{A}ugmented \textbf{L}LM-based \textbf{M}achine \textbf{T}ranslation (REAL-MT) shows promise for knowledge-intensive tasks like idiomatic translation, but its reliability under noisy retrieval contexts remains…

Large Reasoning Models (LRMs) are criticized for the excessively lengthy Chain-of-Thought (CoT) to derive the final answer, suffering from high first-token and overall latency. Typically, the CoT of LRMs mixes multiple thinking units; each…

The Boolean satisfiability (SAT) problem is a computationally challenging decision problem central to many industrial applications. For SAT problems in cryptanalysis, circuit design, and telecommunication, solutions can often be found more…

The rise of code pre-trained models has significantly enhanced various coding tasks, such as code completion, and tools like GitHub Copilot. However, the substantial size of these models, especially large models, poses a significant…

This paper builds and extends on the authors' previous work related to the algorithmic tool, Cylindrical Algebraic Decomposition (CAD), and one of its core applications, Real Quantifier Elimination (QE). These topics are at the heart of…

In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web…

Chain-of-Thought (CoT) prompting improves reasoning in large language models (LLMs), but its reliance on unstructured text limits interpretability and executability in embodied tasks. Prior work has explored structured CoTs using scene or…

Chain-of-Thought (CoT) reasoning enhances Large Language Models (LLMs) by prompting intermediate steps, improving accuracy and robustness in arithmetic, logic, and commonsense tasks. However, this benefit comes with high computational…

Recent progress in reasoning models suggests that generating plausible attempts for research-level mathematics may be within reach, but verification remains a bottleneck, consuming scarce expert time. We hypothesize that a meaningful…