Papers

A framework that persists execution state so a run can be interrupted, survive a crash, and continue must decide what a resume means for effects that already happened. Five widely deployed agent workflow frameworks answer differently, none exposes a machine-checkable contract, and measured behavior violates even the fragments they state. The RESUME CONTRACT states six properties over the persistence API (prefix continuation, effect exactly-once, fork determinism, checkpoint validity, consume-once, recovery determinism), plus fork-intent and liveness obligations. A TLA+ model checks a reference semantics exhaustively, unchanged at scaled bounds (7.4 million states), and the reference conjunction is additionally TLAPS-proved unbounded (196 obligations); a 39-cell fault matrix and two companion modules yield the separating models independence requires. A deterministic, LLM-free harness measures them at pinned releases. LangGraph 1.2.9 durably records a second resume value and never consults it, persists schema-invalid state silently, and re-executes durably recorded work after a real SIGKILL: exactly-once across interrupts, at-least-once across crashes, on one API. CrewAI 1.15.2 re-executes completed effect-bearing methods against its written claim; pydantic-graph 1.x cannot resume after a mid-node crash; no two probed frameworks share a conformance profile. Consume-once holds sequentially and fails under concurrent delivery: k processes resuming one parked interrupt fire the gated effect k times, saturation 1.0 in 36 of 40 cells, and the failure crosses hosts. REMIT, a reference sequencer whose Verus-verified recovery core is line-identical to the shipped executable, repairs the fork and validity cells. The cross-process cell is repaired at the read path: an opt-in gate claims consumption in the shared store, serving one racer and refusing the rest before any node executes.

Explaining the predictions of neural networks is a central challenge in trustworthy AI. Existing explanation methods, such as those based on feature attribution or minimal sufficient sets, typically treat input features as independent, which can yield misleading explanations when inputs exhibit structured dependencies. We address this by formalizing explanations as Halpern-Pearl (HP) actual causes, modeling input dependencies using Boolean Structural Causal Models (SCMs). We compute HP causes by applying bound propagation and branch-and-bound techniques, while providing formal guarantees of completeness and minimality. Our experiments show that we substantially outperform brute-force and ILP baselines in scalability, and outperform heuristic search as graph size grows, computing all minimal actual causes on instances with search spaces of up to $2.3\times10^{13}$ candidate (cause, contingency) pairs, on SCMs with up to 28 nodes, within a 180s per-instance budget. In a case study, we further show that ignoring input dependencies inflates the number of reported causes, 14.9% of which are spurious under our SCM.

Formalisms for hyperproperties provide a solid foundation for studying the verification problem across classes of relational properties, such as those in information flow control (IFC). However, existing formalisms remain limited in expressiveness when it comes to capturing practical aspects of real-world systems. In particular, they do not adequately account for the quantitative nature of such systems. In this paper, we address this gap by revisiting the specification and verification of hyperproperties from a quantitative, measure-based, perspective. We introduce Quantitative Hyper-Logic (QHL), which replaces qualitative trace quantifiers with measure-based ones and extends temporal predicates with richer quantitative expressions. We further study the verification problem from a statistical verification point of view, and develop algorithms for the statistical verification of QHL specifications. For the introduced measure-based quantifiers, we particularly provide an analysis in terms of sample complexity and achievable statistical guarantees. In particular, we show how statistical methods such as Hoeffding's inequality and extreme value theory can be combined to develop statistical verification algorithms for nested measure-based quantifiers. Our approach provides quantitative alternatives for where traditional verification methods become infeasible. We demonstrate both expressiveness and efficacy on benchmarks from quantitative IFC, comparing against qualitative methods.

Combining Bayesian learning and quantitative verification is a powerful toolset for analysing key quantitative properties of software systems, like reliability and response time. However, the accuracy and robustness of verification results strongly depend on the prior knowledge (PK) underlying Bayesian inference. This knowledge reflects original beliefs about the probability of events and typically depends on domain expertise. Using inaccurate or uninformative PK can negatively affect quantitative analysis, yielding incorrect verification results. Our EPIK approach tackles this important challenge by eliciting and embedding PK in quantitative verification equipped with Bayesian estimators. Unlike existing approaches that require PK on formal model transition parameters, EPIK leverages system-level properties that are directly observable and are linked to real-world semantics. EPIK formulates a twofold optimisation problem to derive the distributions of unknown transition parameters and then embeds these distributions to verify new or difficult-to-measure (elusive) properties. The detailed experimental evaluation using multiple variants of real-world case studies and diverse EPIK instantiations shows its effectiveness, flexibility and generality.

The intruder deduction problem is central to symbolic security-protocol analysis: it asks whether an attacker can derive a target message from observed messages using (cryptographic) operators available to the attacker. Although convergent rewrite systems provide canonical normal forms, deduction modulo convergent theories remains undecidable in general, and existing decidable fragments are often shaped by practical cryptographic examples. In this paper, we study deduction from a minimal structural perspective. When all function symbols are unary, terms collapse to words and deduction becomes a right-divisibility problem for semi-Thue systems: given words $u$ and $v$ decide whether there exists $w$ such that $wu \equiv_S v$. We investigate this problem for several classes of semi-Thue systems and prove, to the best of our knowledge, new decidability results for convergent prefix-erasing and convergent suffix-erasing systems. We then extend this perspective to term rewriting systems whose rules erase contexts while lifting selected subterms or variables. Although these classes suggest possible decidable generalisations beyond the unary setting, we show that deduction is already undecidable for a convergent simultaneous variable-lifting system. This exposes both the potential and the limits of extending the right-divisibility results to richer equational theories.

Lokshtanov, Ramanujan, Saurabh, and Zehavi [ICALP 2018] proved that for any CMSO formula $\phi$, testing $\phi$ on arbitrary graphs can be reduced to testing it on $(q,k)$-unbreakable graphs for appropriate parameters. Their proof is non-constructive, and they ask whether it can be made constructive. We prove that this is impossible: specifically, the parameter $q$ cannot be a computable function of $\phi$.

We introduce the category $\omega{\bf FVA}$ of finite-valuation approximable domains, a full subcategory of continuous domains contained in the category of pointed countably based FS-domains. We prove that $\omega{\bf FVA}$ is Cartesian closed and closed under both the subprobabilistic and probabilistic valuation powerdomains. Hence the valuation monads $\mathcal{V}_{\leq 1}$ and $\mathcal{V}_1$ restrict to $\omega{\bf FVA}$, yielding a positive answer to the category-existence form of the Jung–Tix problem, a long-standing open problem in domain theory since the 1990s. In particular, we develop a new factorization-approximation framework for constructing objects from a given class of known objects or structures. Applying this method to the class of subprobabilistic powerdomains over finite posets, we construct the class $\omega{\bf FVA}$ and show that it is closed under Scott-continuous retracts, finite products, function spaces, $\mathcal{V}_{\leq 1}$ and $\mathcal{V}_1$ monads.

We revisit higher-arity atomic concept learning through the geometry of hypercubes and hyperplanes of ground instances. Our starting point is the observation that the ambient r-dimensional hypercube of ground atoms is not structurally uniform. Its logical complexity is organized by hyperplanes: every hyperplane other than the full diagonal collapses into finitely many elementary-equivalence classes, with a bound independent of the term depth, while the full diagonal is exceptional and its class count grows without bound. This asymmetry is not merely geometric. It reflects the reduction-theoretic structure of the concepts themselves. Building on a higher-dimensional framework developed in the author's earlier work, we reinterpret these results through canonical simple concepts, minimal orderings, and representative reductions. This yields a taxonomy of hyperplane behavior in higher dimensions and shows that complexity is localized rather than spread uniformly through the instance space. The paper includes a fully worked binary case, an explicit treatment of the ternary hypercube, and an unpacked account of the reduction machinery that drives the collapse. The three-dimensional case already exhibits the essential phenomenon of orthogonal families, partial diagonals, and the exceptional full diagonal. This geometric-logical perspective clarifies where complexity is concentrated in atomic concept learning and suggests a modern interpretation in terms of constrained hypothesis spaces and structured classification.

Predictive processing theories portray the brain as a hierarchical prediction engine that minimizes prediction error, yet they lack operational definitions for the structure of a "prediction," the standardized response to a prediction error, and the mechanism that maintains consistency across successive updates. Bayesian cognitive science attempts to subsume all uncertainty under probabilistic belief updating, but it presupposes a closed hypothesis space and provides no generative account of how the objects over which probabilities are distributed become discrete, identifiable referents in the first place. This paper introduces Predictive Set Theory (PST), a formal generative framework that reconstructs cognitive architecture from first principles. PST anchors cognition in a minimal set of operations—a sensor formalized as an identity function, set-theoretic state refresh, and three fundamental forms of reference chains (reference, counter-reference, and semi-reference)—and rigorously derives core cognitive functions including state sequences, demand, comparison, efficiency, and finite-horizon probabilistic planning. Rather than modeling neural mechanisms, PST constitutes a design specification for any system that must maintain internal consistency while acting under incomplete information and irreversible risk. The framework offers novel resolutions to classical problems such as Russell's paradox, the cognitive status of Gödelian incompleteness, the grounding of negative feedback, and the comprehension of film editing. The primary purpose of this paper is to establish, through the public academic record, the originality and completeness of the Predictive Set Theory framework.

We show that the tropical semiring over the natural numbers, when used as the grading space in graded coeffect typing, faithfully models the passage of time while simultaneously guaranteeing productivity of well-typed programs. A grade a, when assigned to a function parameter, indicates that the parameter is not necessarily available immediately, but will become available after a time steps. We investigate this idea through two formal systems. We first introduce a graded type system featuring recursive and polymorphic types, and show that, in this setting, a natural restriction on recursive types is sufficient to guarantee productivity, while still allowing the definition of streams and recursive programs on them. In particular, we prove that Nakano's later modality can be embedded directly into our system. We then show that tropical grading naturally suggests a novel form of intersection typing, in which the role traditionally played by sets or multisets of types is instead taken by "timed" sets, i.e., functions assigning to each type A the earliest time, represented as a grade, from which the underlying term is available with type A. For the resulting system, we prove not only that productivity is guaranteed, but that it is also characterized: the typable terms are exactly those with hereditarily head normal forms. Remarkably, the system is recursion-theoretically optimal, i.e., typability can be directly proved to be a $\Pi_0^2$ property in the arithmetical hierarchy.

Linear Temporal Logic (LTL) is one of the most widely adopted languages for specifying temporal extended objectives in AI, with applications ranging from reactive synthesis to stochastic planning in Markov decision processes and reinforcement learning. Traditionally, solving any of these problems requires translating the LTL specification to a nondeterministic automata on infinite words and then determinizing it, a step that is notoriously difficult in theory and in practice. Recent work has introduced LTLf+, which lifts the finite-trace logic LTLf to infinite traces. LTLf+ has the same expressive power as LTL, yet it retains most of the crucial advantages of its base logic LTLf. Most reasoning in LTLf+ rests on finite automata on finite words, for which we have not only a canonical minimal representation but also an efficient determinization procedure. In this work we present the first translation from LTL to LTLf+. We first normalize an LTL formula into the syntactic reactivity fragment of the Manna-Pnueli hierarchy, to create the general fragment-based shape of LTLf+. We then present linear translations for each individual component of that fragment. As a consequence of this translation, the expanding body of techniques developed for LTLf+ now becomes available to many AI problems currently formulated in LTL. We further show that this comes at no asymptotic cost, as the pipeline from LTL to automaton via LTLf+ remains doubly exponential.

We present MechGeo, a Mathlib native agentic framework that jointly addresses faithful autoformalization and certified proof construction for Euclidean geometry. In this framework, GeoFormalizer represents informal problems in GeoIR, deterministically translates them into Lean 4, and iteratively repairs candidate statements using structural diagnostics and semantic evaluation. GeoProver constructs geometric proof plans, derives intermediate lemmas, and selectively algebraizes suitable subgoals through a library verified in Lean. Singular or SymPy may generate algebraic certificates, but all resulting proofs and counterexamples are checked by Lean's kernel. Experiments across seven LLM backbones show substantial improvements in autoformalization, particularly for models with weaker direct translation performance. On 43 historical IMO geometry problems, GeoFormalizer generates formal statements that GeoProver proves in 29 cases; for the remaining 14, it constructs counterexamples verified in Lean and proves all repaired statements after expert correction. Together with IMO 2026 Problem 2, this yields, to the best of our knowledge, the largest reported collection of automated, kernel-checked Lean proofs for IMO geometry problems. On the 14 geometry statements in LEAP's Lean-IMO-Bench, MechGeo proves 12 for the first time, formally refutes the remaining two, and proves both repaired statements. These results establish counterexample guided diagnosis, geometric reasoning, and certified symbolic computation as a practical foundation for trustworthy formal geometry.

In this paper, we consider the parameter synthesis and optimization problem for parametric Markov decision processes (pMDPs), the extension of classical MDPs where exact probability values are replaced by parametric expressions. Computing the rational function $f_{\lsf}$ that maps parameter valuations to the satisfaction value of a PRCTL property $\lsf$ is a computationally expensive task, particularly for pMDPs where the optimal policy may vary across the parameter space. We adopt the scenario approach to efficiently synthesize a probably approximately correct (PAC) approximation $\ApproxFunOfProperty{f}$ of $f_{\lsf}$: by sampling parameter configurations and solving a linear program, we obtain a polynomial approximation whose error margin $\margin$ is guaranteed, with prescribed confidence, for all but an $\errorRate$-fraction of the parameter domain under the sampling distribution. We further show how this PAC framework can be combined with statistical model checking (SMC), enabling the analysis of black-box parametric models. Building on the PAC approximation, we integrate the DIRECT (DIviding RECTangles) algorithm for derivative-free global optimization over the parameter space. We establish conditional optimality-gap guarantees: under explicit Lipschitz and PAC-good-set assumptions, the difference between the true optimum $f_{\lsf}(\parameters^{*})$ and the value found by DIRECT is bounded by a partition-diameter term and, in the PAC case, an additional approximation-error term. An empirical evaluation on 2997 benchmarks focuses on the new DIRECT-based optimization component. The results show that DIRECT variants solve fewer instances than the scenario optimizer, but on their common successful instances they often return slightly better objective values and usually run faster, while remaining close to the scenario values within the PAC margin.

In recent years, there has been rapid development in the foundational study of oracle computability from the perspective of Lawvere-Tierney topologies and their sheaves. In this article, we formulate and analyze the notion of reducibility within the framework of total computability. Then, using sheaf subtoposes derived from oracles in the total computable setting, we establish separations between various hierarchies of logical principles, including the hierarchies of the weak law of excluded middle $\mathbf{WLEM}$, the lessor limited principle of omniscience $\mathbf{LLPO}$, and Markov's principle $\mathbf{MP}$.

A prominent research question in computational logic is how to restrict first-order predicate logic (FO) in such a way that the satisfiability problem becomes decidable. Among others, past efforts have identified two prominent decidable FO fragments of high expressivity: the guarded fragment (GF), and the two-variable fragment (FO2). These fragments are of high interest and crucial importance as they provide significant insights into decidability and expressiveness of other prominent (computational) logics like Modal Logics (MLs)} and various Description Logics (DLs)}, which play a central role in Verification, Knowledge Representation, and other areas. In this article, we show that GF and FO2 can be combined into a new fragment that subsumes both, while maintaining decidability of the satisfiability problem. This fragment, called the triguarded fragment (denoted TGF), is obtained by relaxing the standard definition of GF by requiring guardedness of quantification only for subformulae with three or more free variables. We show that, when restricting the use of equality, satisfiability in TGF is N2ExpTime-complete, dropping to NExpTime-complete when the maximum predicate arity is fixed (a natural assumption in the context of MLs and DLs). We further establish that the problem is NP-complete in terms of data complexity, which is again in line with data complexity results for basic expressive DLs. We observe that many natural extensions of TGF, including the liberal use of equality, lead to undecidability. We also establish that TGF has the finite model property (providing a tight doubly exponential bound on the model size), whence finite satisfiability coincides with satisfiability.

P4 is a domain-specific language for programming protocol-independent packet processors, where packet parsers describe how incoming bit-streams are structured into headers and fields. Building on work by Doenges et al. (2022), we present Octopus, a tool that translates P4 packet parsers into automata and then attempts to (symbolically) check their equivalence. Octopus produces evidence, either in the form of a bisimulation demonstrating equivalence, or a counterexample bit-stream witnessing a behavioral difference between the two parsers. In contrast with earlier work, our tool can check equivalence between non-trivial parsers within minutes, on consumer hardware. We report on the tool's implementation and evaluate its usability in networking contexts.

This report presents mechanized query-bounded soundness for a STARK-style protocol in Isabelle/HOL. An acceptance-preserving embedding connects adaptive, privately randomized Fiat-Shamir transcript producers to an established staged adversary experiment and the original probabilistic verifier. The proof combines FRI correlated-agreement reasoning, Merkle authentication, exact modulo-sampler accounting and weighted-path amplification. Event-sensitive accounting refines the complete error bound without changing the verifier or treating repeated oracle calls as free. For a certified 192-bit prime field, trace length 1024 and 640 query repetitions, the concrete theorem bounds false-endpoint acceptance by $2^{-137}$ for every modeled producer satisfying the uniform syntactic oracle-call bound fs_query_bound $(2^{20})$ P. A separate honest-completeness theorem gives acceptance one for the correct square-sequence endpoint in the same final verifier. These are fixed-statement results in a classical, field-valued random-oracle model with terminating finite-support computation, not an unrestricted 137-bit work-factor guarantee. The development does not prove zero knowledge, knowledge extraction, quantum-query security or correctness of a deployed bit-hash implementation. This report retains earlier proof routes as research history; the accompanying current-results overview and checked theorem manifest identify the principal claims and their assumptions.

Large language models are increasingly used to reason about software vulnerabilities, but their outputs can silently violate domain knowledge, limiting their reliability in safety-critical settings such as medical devices. Prior work either treats that output as a prediction to be scored or constrains it to walks within a single knowledge graph; neither checks whether reasoning over a binary is consistent with an independent body of domain knowledge. We present EntailLLM, which validates each LLM-proposed analyst path by entailment: the path is a traversal of the binary's function call graph, the domain knowledge is represented in a separate graph, and verification aligns the two under temporal annotated logic. Across three CWE classes, four LLMs, three prompting strategies, and seven binaries varying in size from 405 to 12,696 function call-graph nodes, domain knowledge raises pooled entailment from 78% to 98%, with entailment decreasing in only 3% of the experiments. EntailLLM is deployed end-to-end on real medical-device binaries, reaching 98% pooled entailment without per-device tuning. Our system inherits the formal guarantees of generalized annotated logic, providing logical verification of LLM output that is both explainable and grounded in well-defined semantics.