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arxiv: 2606.17693 · v1 · pith:E2XYR7N7new · submitted 2026-06-16 · 💻 cs.LO

Verifying LTL for Infinite State Systems via Termination Analysis

Nils Lommen , Moritz Leven Rosarius , J\"urgen Giesl This is my paper

Pith reviewed 2026-06-26 22:34 UTC · model grok-4.3

classification 💻 cs.LO
keywords LTL model checkinginfinite-state systemstermination analysisfair terminationautomata-based reductionprogram verificationmodel checking
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The pith

Existing termination analysis tools can verify LTL properties on infinite-state systems by reducing the task to fair termination.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to demonstrate that tools built for termination analysis work well for LTL model checking when systems have infinitely many states. It does so by building a framework that first converts the LTL question into an equivalent fair termination question through an automata construction, then hands the resulting problem to termination provers. Experiments indicate that this route produces results on par with tools written specifically for LTL model checking. A reader would care because many real systems, such as programs with unbounded integers or counters, fall into the infinite-state category where specialized LTL tools have historically been limited.

Core claim

The central claim is that the well-known automata-based reduction turns LTL model checking of infinite-state systems into a fair termination problem that existing termination tools can solve, and that the resulting procedure matches the performance of current state-of-the-art LTL model checkers on the same benchmarks.

What carries the argument

MoAT, the framework that applies the automata-based reduction from LTL model checking to fair termination and delegates the resulting problems to termination analysis tools.

If this is right

  • LTL model checking of infinite-state systems becomes an instance of fair termination analysis.
  • Termination provers developed for integer programs and similar domains can be applied directly to decide LTL questions.
  • Both positive and negative answers to LTL properties can be obtained through the same termination machinery.
  • Performance of the combined procedure reaches the level of dedicated LTL model checkers on standard benchmarks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Advances made in termination analysis would automatically improve the LTL model checking method without further changes to the reduction.
  • The same reduction strategy might be reused for other temporal properties once they are shown to reduce to fair termination.
  • Extending the set of back-end termination tools could increase the fraction of problems decided without altering the front-end reduction.

Load-bearing premise

The automata reduction from LTL model checking to fair termination stays sound and complete for infinite-state systems and the termination tools decide the generated problems without introducing errors that flip the overall answer.

What would settle it

An infinite-state system together with an LTL formula such that the reduced fair termination instance is answered incorrectly by the termination tools, producing a model-checking verdict that differs from the true satisfaction of the formula.

read the original abstract

We show that existing tools for termination analysis are extremely well suited for LTL model checking of infinite state systems. To this end, we present a framework MoAT which uses the well-known automata-based approach and reduces the LTL model checking problem to fair termination. To prove or disprove fair termination, it then calls the termination tools KoAT and LoAT in the backend. Our experiments show that in this way, MoAT is on par with existing state-of-the-art tools for LTL model checking of infinite state systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript presents MoAT, a framework that reduces LTL model checking for infinite-state systems to the problem of fair termination via the standard automata-based construction and delegates the resulting queries to the termination tools KoAT and LoAT. Experiments are reported to show that MoAT performs on par with existing state-of-the-art LTL model checkers for infinite-state systems.

Significance. If the reduction is shown to be sound and complete, the work would establish that mature termination provers can be repurposed for LTL verification without loss of precision, providing an alternative route that leverages existing infrastructure. The reported experimental parity supplies concrete evidence of practical competitiveness.

major comments (1)
  1. [Reduction section (automata construction and fair termination)] The central claim rests on the automata reduction preserving both soundness and completeness when lifted to infinite-state systems and when the generated fair-termination instances are handed to KoAT/LoAT; no explicit theorem, proof sketch, or argument addressing potential precision loss from the Büchi product or from the termination provers' approximations appears in the reduction section, which is load-bearing for the experimental verdict.
minor comments (1)
  1. [Experiments] The experimental section would benefit from an explicit statement of the benchmark selection criteria and how fairness constraints are encoded in the test suite.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and the identification of a point that can strengthen the presentation. We address the major comment below.

read point-by-point responses

  1. Referee: [Reduction section (automata construction and fair termination)] The central claim rests on the automata reduction preserving both soundness and completeness when lifted to infinite-state systems and when the generated fair-termination instances are handed to KoAT/LoAT; no explicit theorem, proof sketch, or argument addressing potential precision loss from the Büchi product or from the termination provers' approximations appears in the reduction section, which is load-bearing for the experimental verdict.

    Authors: The reduction in MoAT follows the standard automata-theoretic construction that translates an LTL formula into a Büchi automaton and reduces model checking to fair termination of the product system. This construction is sound and complete for arbitrary transition systems (finite or infinite) because language equivalence is preserved independently of state-space cardinality; the same reduction is used in the finite-state case and in other infinite-state LTL tools. We did not restate a full proof because the construction is textbook (Vardi-Wolper and subsequent literature), but we accept that an explicit theorem and short argument would improve clarity. In revision we will insert a dedicated paragraph (or small subsection) stating: (i) the product construction yields an equivalent fair-termination problem, (ii) no precision is lost in the Büchi product itself, and (iii) any incompleteness stems solely from the underlying termination prover, exactly as in competing tools. This addition directly addresses the load-bearing claim without altering the technical content. revision: yes

Circularity Check

0 steps flagged

No circularity; standard automata reduction to fair termination with external provers

full rationale

The paper reduces LTL model checking to fair termination via the well-known automata-based approach and invokes the independent termination tools KoAT and LoAT as black-box backends. No self-definitional equations, fitted parameters renamed as predictions, or load-bearing self-citations appear in the derivation chain. The central claim is supported by experimental comparison against external state-of-the-art LTL tools, which constitutes an independent benchmark rather than a closed loop. The soundness/completeness question raised by the skeptic concerns external verification of the reduction for infinite-state systems, not circular dependence on the paper's own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the approach rests on the standard automata construction for LTL and the soundness of the cited termination tools.

pith-pipeline@v0.9.1-grok · 5613 in / 1039 out tokens · 31452 ms · 2026-06-26T22:34:24.723814+00:00 · methodology

discussion (0)

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Reference graph

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