arXiv subjects

Mikoláš Janota

Publications and source records attributed to Mikoláš Janota.

At least 19 recordsLinked to original sources

arXiv2026

Proving at Scale for Universal Algebra

We introduce SemiBase, a project that computes and formally certifies finite identity bases for small semigroups. Deciding finite basability is undecidable for finite algebras and remains open for finite semigroups. The task requires a proof that a candidate basis is complete, or a proof that none exists, rather than a single first-order validity query. LLM-guided agents search for these proofs; a referee agent rebuilds them from source, and the Lean kernel checks the resulting corpus in a final audit. Humans choose targets and approve final outcomes. We certify every semigroup of order at most 6: all 1309 semigroups of order at most 5 and all 15973 of order 6, including proofs that the four known nonfinitely based semigroups have no finite basis. The bases for order 6 define 505 distinct varieties, whose inclusion order Vampire determines except for four pairs. The resulting catalogue is a machine-checked account of results scattered across the literature and a tested foundation for order 7.

cs.LO↗

arXiv2026

Compact Partial Symmetry Breaking for Graph Search Problems

Symmetry breaking in graph search problems remains challenging: complete symmetry breaking constraints are typically exponential in size, while partial approaches trade precision for scalability. We introduce a strength-driven, redundancy-aware methodology for constructing compact partial symmetry breaking constraints based on graph patterns. Each pattern corresponds to a Boolean clause over equality literals and can be integrated directly into CP or SAT models. Our approach incrementally selects strong, non-redundant graph patterns, yielding partial symmetry breaks that achieve substantial pruning of non-canonical graphs while remaining compact in size. This provides a principled framework for deriving lightweight partial symmetry breaking constraints which are significantly more precise than all published state-of-the-art alternatives. We evaluate the proposed constraints on graph instances with up to 25 vertices using a redundancy ratio metric. The resulting partial symmetry breaks constitute only a small fraction of the size of complete symmetry breaking constraints, while delivering significant performance improvements across several graph search benchmarks compared to previously defined partial symmetry breaking methods.

cs.LO↗

arXiv2026

Reintroducing the Second Player in EPR

We present a PSPACE-complete fragment of first order logic we call QEALM (QBF-like EPR by Alternating Level-ordered Miniscoping). Unlike other well-known fragments it is closer to QBF (Quantified Boolean Formulas) in nature because it has game-like alternations and can be restricted to complete problems for the polynomial hierarchy. QEALM is a natural first-order analogue to QBF just as EPR (Effectively Propositional logic) is a first-order analogue to Dependency QBF. We prove the PSPACE and Polynomial Hierarchy completeness theorems of QEALM along with several other nice properties such as closure under Robinson's resolution and retained hardness after intersection with Schaefer fragments. We identify problems in the TPTP library that fall into this fragment and their level in the polynomial hierarchy.

cs.LO↗

arXiv2026

Vibe-Coded and Tuned: A State-of-the-Art SMT Solver for QF-LRA

This paper presents the SMT solver primo, which is fully vibe-coded and then parameter-tuned, achieving state-of-the-art results on linear real arithmetic (QF-LRA). The performance of primo is achieved by a systematic literature survey, repeated profiling, and parameter tuning. The resulting solver outperforms the winner of the QF-LRA track of SMT-COMP~2026. This confirms that vibe-coding of automated reasoning tools will enable us to make great strides in the future.

cs.LO↗

arXiv2026

SAT-based Encodings for Optimal Decision Trees with Explicit Paths

Decision trees play an important role both in Machine Learning and Knowledge Representation. They are attractive due to their immediate interpretability. In the spirit of Occam's razor, and interpretability, it is desirable to calculate the smallest tree. This, however, has proven to be a challenging task and greedy approaches are typically used to learn trees in practice. Nevertheless, recent work showed that by the use of SAT solvers one may calculate the optimal size tree for real-world benchmarks. This paper proposes a novel SAT-based encoding that explicitly models paths in the tree, which enables us to control the tree's depth as well as size. At the level of individual SAT calls, we investigate splitting the search space into tree topologies. Our tool outperforms the existing implementation. But also, the experimental results show that minimizing the depth first and then minimizing the number of nodes enables solving a larger set of instances.

cs.LO↗

arXiv2026

Solving QBF by Clause Selection

Algorithms based on the enumeration of implicit hitting sets find a growing number of applications, which include maximum satisfiability and model based diagnosis, among others. This paper exploits enumeration of implicit hitting sets in the context of Quantified Boolean Formulas (QBF). The paper starts by developing a simple algorithm for QBF with two levels of quantification, which is shown to relate with existing work on enumeration of implicit hitting sets, but also with recent work on QBF based on abstraction refinement. The paper then extends these ideas and develops a novel QBF algorithm, which generalizes the concept of enumeration of implicit hitting sets. Experimental results, obtained on representative problem instances, show that the novel algorithm is competitive with, and often outperforms, the state of the art in QBF solving.

cs.LO↗

arXiv2026

Solving QBF with Counterexample Guided Refinement

We propose two novel approaches for using Counterexample-Guided Abstraction Refinement (CEGAR) in Quantified Boolean Formula (QBF) solvers. The first approach develops a recursive algorithm whose search is driven by CEGAR (rather than by DPLL). The second approach employs CEGAR as an additional learning technique in an existing DPLL-based QBF solver. Experimental evaluation of the implemented prototypes shows that the CEGAR-driven solver outperforms existing solvers on a number of families in the QBF-LIB and that the DPLL solver benefits from the additional type of learning. Thus this article opens two promising avenues in QBF: CEGAR-driven solvers as an alternative to existing approaches and a novel type of learning in DPLL.

cs.LO↗

arXiv2026

Revisiting Incremental Linearization for Nonlinear Integer Arithmetic

Incremental Linearization has previously been proposed for solving SMT problems over quantifier-free nonlinear integer arithmetic and has proven effective despite its conceptual simplicity. In this paper, we introduce a revised axiom set that improves convergence on polynomial constraints built from higher-degree monomials, such as powers and mixed products, a class of problems on which prior axiomatizations struggled. We present a standalone implementation built on top of Z3 for linear integer arithmetic and evaluate it on the NIA benchmark set from SMT-LIB. Our results show that the approach is competitive with state-of-the-art solvers overall and substantially outperforms them on benchmarks dominated by such polynomial constraints.

cs.LO↗

arXiv2026

A Universal Textual Merge Strategy Based on Tokens for Version Control Systems

Merging is a core operation in version control systems such as Git, but traditional line-based algorithms often yield spurious conflicts, particularly in the presence of refactorings or parallel edits. While syntax- and semantics-aware merging approaches can reduce conflicts, they introduce drawbacks such as loss of formatting, dependence on language-specific parsers, and limited flexibility across heterogeneous artifacts. To address this gap, we present Summer, a novel textual token-based merge algorithm independent of document formats. Dividing text into tokens, our approach formulates token-level changes in one branch into string-rewriting rules and move rules, and applies these rules to the text of the other branch to construct a merge. Despite being independent on programming languages, our move rules model extracting and inlining functions. We evaluated Summer on ConflictBench, a large benchmark of real-world merge scenarios, comparing it with five pioneering merge tools across Java and non-Java files. Experimental results show that Summer achieved the highest 36% accuracy in reproducing merges verbatim identical to developers', and ranked second in semantic accuracy.

cs.SE↗

arXiv2026

Breaking Symmetries with Involutions

Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered too weak to be of practical use. Recently, the concept of graph patterns has been introduced and provides a concise representation for (large) sets of non-canonical graphs, i.e.\ graphs that are not lex-leaders and can be excluded from search. In particular, four (specific) graph patterns apply to identify about 3/4 of the set of all non-canonical graphs. Taking this approach further we discover that graph patterns that derive from permutations that are involutions play an important role in the construction of symmetry breaks for graphs. We take advantage of this to guide the construction of partial and complete symmetry breaking constraints based on graph patterns. The resulting constraints are small in size and strong in the number of symmetries they break.

cs.LO↗

arXiv2026

Breaking Symmetries from a Set-Covering Perspective

We formalize symmetry breaking as a set-covering problem. For the case of breaking symmetries on graphs, a permutation covers a graph if applying it to the graph yields a smaller graph in a given order. Canonical graphs are those that cannot be made smaller by any permutation. A complete symmetry break is then a set of permutations that covers all non-canonical graphs. A complete symmetry break with a minimal number of permutations can be obtained by solving an optimal set-covering problem. The challenge is in the sizes of the corresponding set-covering problems and in how these can be tamed. The set-covering perspective on symmetry breaking opens up a range of new opportunities deriving from decades of studies on both precise and approximate techniques for this problem. Application of our approach leads to optimal LexLeader symmetry breaks for graphs of order $n\leq 10$ as well as to partial symmetry breaks which improve on the state-of-the-art.

cs.LO↗

arXiv2026

LLM2SMT: Building an SMT Solver with Zero Human-Written Code

Whether LLMs can reason or write software is widely debated, but whether they can write software that itself reasons is largely unexplored. We present a case study in which an LLM coding agent builds a complete DPLL(T)-style SMT solver for QF_UF with zero human-written code. The solver implements the Nieuwenhuis-Oliveras congruence closure algorithm, includes preprocessing, and emits Lean proofs for unsatisfiable instances. We describe the development process and key challenges, and show that the resulting solver is competitive on SMT-LIB benchmarks.

cs.LO↗

arXiv2026

Geometric Reasoning in the Embedding Space

In this contribution, we demonstrate that Graph Neural Networks and Transformers can learn to reason about geometric constraints. We train them to predict spatial position of points in a discrete 2D grid from a set of constraints that uniquely describe hidden figures containing these points. Both models are able to predict the position of points and interestingly, they form the hidden figures described by the input constraints in the embedding space during the reasoning process. Our analysis shows that both models recover the grid structure during training so that the embeddings corresponding to the points within the grid organize themselves in a 2D subspace and reflect the neighborhood structure of the grid. We also show that the Graph Neural Network we design for the task performs significantly better than the Transformer and is also easier to scale.

cs.LG↗

arXiv2026

Case Study: Saturations as Explicit Models in Equational Theories

Automated theorem provers (ATPs) can disprove conjectures by saturating a set of clauses, but the resulting saturated sets are opaque certificates. In the unit equational fragment, a saturated set can in fact be read as a convergent rewrite system defining an explicit, possibly infinite, model -- but this is not widely known, even amongst frequent users of ATPs. Moreover, ATPs do not emit these explicit certificates for infinite (counter-)models. We present such a certificate construction in full, implement it in Vampire and E, and apply it to the recent Equational Theories Project, where hundreds of implications do not admit finite countermodels. The resulting rewrite systems can be checked for confluence and termination by existing certified tools, yielding trustworthy countermodels.

cs.LO↗

arXiv2026

Inductive Satisfiability Certification for Universal Quantifiers and Uninterpreted Function Symbols

The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about arrays. Yet the satisfiability of such formulas is, in general, undecidable. In practice, SMT solvers are often successful in the unsatisfiable case, using heuristics. However, in the satisfiable case, they rely on explicit model construction, which fails for formulas whose smallest model is not small enough. We introduce an alternative approach that certifies satisfiability using induction arguments, and apply it to the case of linear integer arithmetic. The resulting algorithm is able to prove satisfiability of formulas that are out of reach for current SMT solvers.

cs.LO↗

arXiv2025

Machine Learning for Quantifier Selection in cvc5

In this work we considerably improve the state-of-the-art SMT solving on first-order quantified problems by efficient machine learning guidance of quantifier selection. Quantifiers represent a significant challenge for SMT and are technically a source of undecidability. In our approach, we train an efficient machine learning model that informs the solver which quantifiers should be instantiated and which not. Each quantifier may be instantiated multiple times and the set of the active quantifiers changes as the solving progresses. Therefore, we invoke the ML predictor many times, during the whole run of the solver. To make this efficient, we use fast ML models based on gradient boosting decision trees. We integrate our approach into the state-of-the-art cvc5 SMT solver and show a considerable increase of the system's holdout-set performance after training it on a large set of first-order problems collected from the Mizar Mathematical Library.

cs.AI↗

arXiv2025

Model-Based Diagnosis with Multiple Observations: A Unified Approach for C Software and Boolean Circuits

Debugging is one of the most time-consuming and expensive tasks in software development and circuit design. Several formula-based fault localisation (FBFL) methods have been proposed, but they fail to guarantee a set of diagnoses across all failing tests or may produce redundant diagnoses that are not subset-minimal, particularly for programs/circuits with multiple faults. This paper introduces CFaults, a novel fault localisation tool for C software and Boolean circuits with multiple faults. CFaults leverages Model-Based Diagnosis (MBD) with multiple observations and aggregates all failing test cases into a unified Maximum Satisfiability (MaxSAT) formula. Consequently, our method guarantees consistency across observations and simplifies the fault localisation procedure. Experimental results on three benchmark sets, two of C programs, TCAS and C-Pack-IPAs, and one of Boolean circuits, ISCAS85, show that CFaults is faster at localising faults in C software than other FBFL approaches such as BugAssist, SNIPER, and HSD. On the ISCAS85 benchmark, CFaults is generally slower than HSD; however, it localises faults in only 6% fewer circuits, demonstrating that it remains competitive in this domain. Furthermore, CFaults produces only subset-minimal diagnoses of faulty statements, whereas the other approaches tend to enumerate redundant diagnoses (e.g., BugAssist and SNIPER).

cs.SE↗

arXiv2025

Minimizing the Weighted Number of Tardy Jobs: Data-Driven Heuristic for Single-Machine Scheduling

Existing research on single-machine scheduling is largely focused on exact algorithms, which perform well on typical instances but can significantly deteriorate on certain regions of the problem space. In contrast, data-driven approaches provide strong and scalable performance when tailored to the structure of specific datasets. Leveraging this idea, we focus on a single-machine scheduling problem where each job is defined by its weight, duration, due date, and deadline, aiming to minimize the total weight of tardy jobs. We introduce a novel data-driven scheduling heuristic that combines machine learning with problem-specific characteristics, ensuring feasible solutions, which is a common challenge for ML-based algorithms. Experimental results demonstrate that our approach significantly outperforms the state-of-the-art in terms of optimality gap, number of optimal solutions, and adaptability across varied data scenarios, highlighting its flexibility for practical applications. In addition, we conduct a systematic exploration of ML models, addressing a common gap in similar studies by offering a detailed model selection process and providing insights into why the chosen model is the best fit.

cs.LG↗