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996 records · Page 3Linked to original sources
arXiv2026

Beyond Lemma Sharing -- Novel Parallelization Strategies for Property Directed Reachability

Property Directed Reachability (PDR) is a commonly used technique for automated hardware model checking, yet efficiently parallelizing it remains a significant challenge. Existing approaches, such as lemma sharing, often suffer from limited scalability as processor counts increase. In this work, we present two novel sharing-based parallelization strategies, preemptive propagation and ARPOS, and compare their performance with classical lemma sharing. To this end, we develop an asynchronous MPI-based message passing framework for the state-of-the-art rIC3 hardware model checker. Experimental results on the 2025 Hardware Model Checking competition benchmark demonstrate that our preemptive propagation strategy yields a significant performance boost over classical lemma sharing.

cs.DC↗
arXiv2026

Constructive solvability and the P versus NP problem

The relation between the computational complexity class NP and other complexity classes is addressed in the context of provability and limitations on the possibility of finding sound axioms for formal theories. We construct a family D of decision problems and show that under a certain finiteness condition, D contains a problem which is in NP. Further, it is shown that if the term ``constructible theory'' is defined in a way satisfying a specific natural condition, then no constructible and sound theory verifies a solution algorithm for any of the problems in D. Arguably, this solves the P versus NP problem under a constructive interpretation. The relation to classical proofs of NP $\subseteq$ EXPTIME is discussed. These proofs tacitly use an assumption which may fail for problems in D.

cs.CC↗
arXiv2026

Outrunning Big KATs: Efficient Decision Procedures for Variants of GKAT

This paper presents several efficient decision procedures for trace equivalence of GKAT automata, which make use of on-the-fly symbolic techniques via SAT solvers. To demonstrate applicability of our algorithms, we designed symbolic derivatives for CF-GKAT, a practical system based on GKAT designed to validate control-flow transformations. We implemented the algorithms in Rust and evaluated them on both randomly generated benchmarks and real-world control-flow transformations. Indeed, we observed order-of-magnitude performance improvements against existing implementations for both KAT and CF-GKAT. Notably, our experiments also revealed a bug in Ghidra, an industry-standard decompiler, highlighting the practical viability of these systems.

cs.PL↗
arXiv2026

Typed Flexible-Arity Slotted E-Graphs: A Soundness Construction and an Alloy Case Study

Slotted e-graphs represent open terms modulo consistent renaming, while algebraic operators benefit from canonical sequence, bag, or set children. We compose the two at a specification level: typed slot-mapped invocations inhabit operator-declared ports whose sibling quotient and recursive flattening licenses are certified separately. A generic finite quotient presentation proves exactness of its least-orbit normal form, while certified records specify effective-support kernel extraction and collision. For abstract obligation traces carrying local endpoint certificates, we prove finite-unfolding equational soundness. An Alloy case study compares seven related pipeline arms on a frozen corpus and a controlled transformation suite. Its measurements characterize bounded capability and structural consolidation; they do not establish refinement of the Java artifact or experimental replay against the formal model.

cs.PL↗
arXiv2026

Computational free will as global selection: from sheaf-theoretic gluing to a conditional separation of P and NP

We formalise computational free will by separating locally constrained admissibility from the selection of one global continuation. Global sections of a finite choice presheaf form an admissible set, GLUE; SELECT singles out the continuation realised at a pre-identified occurrence. A uniform trace relation certifies that continuation efficiently after the act, although it is assumed not to be uniformly anticipable in polynomial time from the prior occurrence input. Under explicit uniformity, balance, historical-completeness, and unique-projection assumptions, this trace defines a total FNP search relation with no deterministic polynomial-time selector. Thus existence of computational free will in the stated sense implies a separation between polynomially verifiable and polynomially solvable search, and hence that P differs from NP. The result is conditional and gives no unconditional class separation.

cs.LO↗
arXiv2026

Solving Fuzzy Satisfiability via Mixed-Integer Non-Linear Programming

This paper introduces SATFuL, a SAT solver for fuzzy logics. In contrast to the Boolean case, for which numerous SAT solvers exist, the SAT problem for fuzzy logics has attracted less attention, even though these tools have interesting applications. Unlike existing SAT solvers for fuzzy logics, SATFuL uses MINLP (Mixed Integer Non-Linear Programming) solvers to check the satisfiability of fuzzy formulas. This approach offers certain benefits; for instance, our tool can handle all major variations of fuzzy propositional logic, whereas other fuzzy solvers are usually tailored to specific versions of fuzzy logic. We conduct some experiments and demonstrate that the performance of our tool is comparable with state-of-the-art fuzzy solvers for Lukasiewicz logic, and outperforms available solvers for Product logic. The approach is sound and complete and can be easily extended to accommodate new fuzzy operators.

cs.LO↗
arXiv2026

Languages and Recognition in a Category with Factorisation

Language recognition by homomorphisms is a central construction of algebraic language theory. Initially studied for monoids and semigroups, it has subsequently been expanded to other algebraic structures. Our new categorical account is based on fibrations, which have already seen other applications in automata theory. Languages and surjective homomorphisms give indeed rise to two fibrations, and the notion of language recognition is stable under reindexing. We develop this framework in a category with a factorisation system and address two main technical questions in the fibrational setting. First, we provide sufficient conditions under which languages have syntactic quotients (which is a generalisation of syntactic congruences) and we show how such quotients can be described in some concrete cases using a result by Slomiński. Second, we introduce sufficient conditions under which (regular) languages are closed under certain J-limits and J-colimits.

cs.FL↗
arXiv2026

Climate Physics Dynamic Matching

Deep generative models such as flow matching and diffusion models have shown potential for learning complex dynamical systems, but typically act as black boxes that neglect underlying physical structure, while physics-based models governed by partial differential equations are often incomplete due to missing source terms, or uncertain parametrisations. We present Climate Physics Dynamic Matching (ClimPhyDM), a variational simulation-free dynamics informed framework for weather forecasting that combines an advection-type physics prior with data-driven components in a variational framework. % to capture the stochasticity and multi-modality of unresolved atmospheric dynamics. On the ERA5 benchmark at hourly (42-hour) and monthly (5-month) resolutions, ClimPhyDM outperforms ClimODE, and GB-DM, keeping the lower error at extended horizon, indicating improved temporal stability and resistance to error accumulation, while its simulation-free paradigm also enables training on a single modest 12 GB consumer GPU.

stat.AP↗
arXiv2026

On Synthesis of Metric Interval Temporal Logics

Automated mining of formal specifications is vital for verifying real-time systems. However, existing passive learning approaches remain restricted to deterministic specifications or limited fragments of Timed Regular Expressions (TRE). To our knowledge, this paper presents the first framework to tackle \emph{precise} passive learning for an expressive timed logic, \emph{Metric Interval Temporal Logic} (MITL) without relying on predefined templates or restricted logic fragments. Our approach formally reduces the timed learning problem into a scalable untimed one. By identifying quantitative timing differences between positive and negative traces, we synthesise precise timed constraints and inject them as new Boolean atomic propositions. This embeds timing into the alphabet, delegating the complex formula evaluation to highly optimised, off-the-shelf untimed LTL tools. Crucially, our framework is complete, guaranteeing a separating specification can always be found. We evaluate our implementation across several benchmarks, demonstrating the effectiveness of our approach.

cs.LO↗
arXiv2026

Specification-Guided Path Shortcutting for Efficient Probabilistic Model Checking

Given the safety-critical nature of many embedded systems, their safety assurance is essential. Because such systems are typically stochastic, probabilistic model checking is a particularly important technique. However, there is a well-known scalability issue due to state-space explosion, especially when verifying complex properties. To mitigate this issue, we propose specification-guided path shortcutting for probabilistic systems, focusing on Markov chains (MCs) and $ω$-regular properties. The key idea is that, when the verified property is fixed, certain sequences of transitions in an MC can be replaced with a single transition without changing the satisfaction probability, and thus, we can reduce the state space of the MC. We implement the proposed path shortcutting and evaluate its contribution to the performance of probabilistic model checking, using Storm as the baseline model checker. The results suggest that our approach often outperforms the baseline, particularly on benchmark instances with complex specifications.

cs.LO↗
arXiv2026

From Contexts to Values: Context-Dependent Defeat in Abstract Argumentation

In value-based argumentation, an audience's ordering of values decides which attacks succeed as defeats. In many settings the deciding factor is not the audience but the circumstances: the same attack may succeed at one procedural stage, or under one regulation, and fail at another. Context-dependent argumentation frameworks (CDAFs), a model we recently introduced, capture this directly: one attack relation and a defeat function that switches each attack on or off per context, so every context induces an ordinary Dung framework. This raises a reduction question: can one value assignment with per-context orderings reproduce the defeat function, collapsing the CDAF into a VAF? We present a polynomial-time decision procedure for this question and map the harder neighbouring problems, with upper bounds from NP to $Σ^p_3$. We also present a validated reference implementation and a measurement: representability is rare and falls fast with the number of contexts.

cs.AI↗
arXiv2026

Taming the Search Space: Solving and Generating Hitori and Binairo Puzzles

This paper investigates solving and generation techniques for the logic puzzles Hitori and Binairo. Two solving paradigms are compared: backtracking with domain-specific optimizations, and SAT-based solving via conjunctive normal form encodings. An empirical evaluation analyzes runtime, explored search nodes, and branching factor across varying puzzle sizes. To support systematic benchmarking in the evaluation, generators capable of producing valid and uniquely solvable puzzle instances are developed. Results indicate that constraint propagation is the most effective backtracking optimization, substantially reducing the effective branching factor, search tree size, and thus runtime. Heuristic variable ordering and scoring strategies provide additional improvements. For Binairo, the SAT-based approach solves all evaluated instances within low runtime, while optimized backtracking fails to solve difficult puzzle instances within the timeout. For Hitori, propagation-based backtracking achieves the best results, while for the SAT-based approach the iterative connectivity check takes up the majority of the runtime, failing difficult puzzle instances.

cs.LO↗
arXiv2026

A note on the reduction from LTLf to LTL

LTLf, a finite word variant of LTL, can be reduced to LTL by introducing a new atomic proposition indicating the prefix of the infinite words that correspond to the finite words that the original LTLf formula was considering. Such a reduction was originally proposed by De Giacomo and Vardi (IJCAI'13). However, while any LTL formula reduced from LTLf describes an obligation property in the hierarchy of Manna and Pnueli (PODC'90), the aforementioned reduction does not provide an LTL formula that belongs to the syntactic obligation fragment of LTL. This note shows how the reduction was fixed in Spot in order to ensure that the resulting LTL formula is always a syntactic obligation. Doing so allows algorithms specialized to syntactic obligation to be used on LTLf formulas. For instance, in previous work (CAV'26) we described a specialized translation from syntactic obligations to minimal, weak, deterministic Büchi automata that would not be usable with the original reduction.

cs.FL↗
arXiv2026

Intuitionistic Unitary Linear Logic: A Proof-Theoretical Approach to Purely Quantum Higher-Order

Although the circuit model for quantum computation is well established, it is incapable of representing non-causal higher-order quantum processes such as the quantum switch. If several models of non-causal quantum computation have been considered in the literature, the approaches have so far only been focusing on the physicality of such processes, using matrices and other techniques from linear algebra. If these approaches are expressive, they however only provide a static and monolithic understanding of these processes. In this article, we propose a new formalism for non-causal, higher-order quantum processes. Based on a Curry-Howard interpetation, our proposal offers a computational interpretation that is both compositional and modular. In particular, we present Intuitionistic Unitary Linear Logic (IULL), a logic based on linear logic focusing on conservation of unitarity for higher order terms. We prove the coherence of IULLL, its completeness with regard to unitaries, and the admissibility of its cut rules. We finally discuss the validity of our approach by revisiting known non-causal quantum processes with IULL.

cs.LO↗
arXiv2026

Robust PAC Learning of Concurrent Stochastic Games

We introduce the first Probably Approximately Correct (PAC) learning framework for general-sum concurrent stochastic games (CSGs) with transition uncertainty, while addressing the challenge of Nash equilibrium (NE) existence. Our algorithm maintains data-driven $L^1$ confidence sets over transition kernels and solves a robust CSG to compute a social-welfare optimal $\varepsilon$-NE, using a robust MDP-based exploration mechanism to drive joint state-action coverage. Crucially, we introduce a Nash margin characterisation that enables principled reasoning about equilibrium existence: the framework either returns an $\varepsilon$-approximate NE whose social-welfare value is $\varepsilon$-close to optimal, or provides a sound certificate that no exact NE exists. Under a minimum reachability condition $p_{\mathrm{reach}}>0$ over relevant state-action pairs, the algorithm terminates after a polynomial number of trajectory samples, with sample complexity $\widetilde{O}\left( {R_{\max}^2 H^4 |S|^2 |A| / (p_{\mathrm{reach}} \varepsilon^2)} \right)$. Empirical results on benchmark CSGs demonstrate near-optimal performance, correct handling of equilibrium (non-)existence, and sample complexity consistent with theory.

cs.LG↗
arXiv2026

On the Depth Scalability of Logic Gate Networks

Logic Gate Networks (LGNs) compute through compositions of Boolean operations, yet existing LGNs do not reliably benefit from increased depth. We identify two causes: optimization collapse and topology-induced degradation of output-specific credit that persists even after skip-biased initialization and straight-through estimation stabilize training. We introduce Input-Anchored Logic Gate Networks (IALGNs), in which each gate combines a private hidden spine with a direct input anchor. This topology prevents output-path merging while retaining input access at every layer. Credit diagnostics show that random wiring dilutes or conflicts output-specific gradients, whereas IALGN maintains usable and coherent credit. Random-$k_x$ relaxation improves anchor selection without relaxing the spine. Across MNIST, CIFAR-10, and CIFAR-100, IALGN exhibits consistent fixed-width depth--accuracy scaling up to 150 layers, while alternative topologies saturate or degrade. Linear probes, topology ablations, and operation-aware analysis show that trained IALGNs preserve private states and apply sparse anchor-conditioned updates. These results indicate that scalable LGN depth requires both stable optimization and credit-preserving information access.

cs.LG↗
arXiv2026

Polynomial Invariants for Probabilistic Transition Systems with Unbounded Support

We study the synthesis of polynomial invariants for probabilistic transition systems (PTS) based on martingale theory. We present tractable methods to verify that such polynomials are indeed invariants, in the sense that their expected value upon termination is the same as their value at the start of the computation. We do this by applying the Optional Stopping Theorem (OST) in the form of a specific precondition. This precondition requires the existence of an integrable dominating function for the martingale expression, which implies uniform integrability; we refer to this condition as dui. For linear PTS we simplify the dui property to proving finiteness of the expected value of an expression depending on the update matrix, the degree of the martingale expression, and the stopping time. Specifically, if all random samples have finite moments and we can verify a moment bound on the runtime of a linear loop, then we can automatically synthesise polynomial loop invariants that satisfy the OST. Notably, dui allows for the sampled distributions to have unbounded support, which is a novel contribution to the field.

cs.LO↗
arXiv2026

MathAdv: What Theorem Provers Know, Reason, Formalize, and Generalize

Formal theorem proving enables machine-verifiable evaluation of mathematical reasoning, yet existing benchmarks often emphasize aggregate proof accuracy, concentrate on a narrow range of mathematics, and provide limited evidence of robustness to equivalent reformulations. We introduce MathAdv, a diagnostic benchmark spanning 13 domains across undergraduate- and graduate-level mathematics. Alongside Lean 4 theorem proving, MathAdv provides up to three auxiliary tasks: multiple-choice questions that probe mathematical knowledge, fill-in-the-blank problems that isolate informal reasoning, and expert-crafted transformations that test robustness to problem presentation. Our evaluation of contemporary theorem provers yields four findings: formalization remains a major bottleneck; performance varies substantially across mathematical domains; natural-language guidance helps general-purpose LLMs but can hinder proof-specialized models; and mathematically equivalent reformulations expose substantial robustness limitations. Together, these results show how component-wise evaluation can reveal model capabilities and failure modes that aggregate theorem-proving accuracy obscures. The dataset and evaluation scripts are available at https://github.com/margotyjx/MathAdv.git.

cs.CL↗