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Deciding Probabilistic Automata Weak Bisimulation in Polynomial Time

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Holger Hermanns, Andrea Turrini

Formal Languages and Automata Theory · Submitted 2 May 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this work we close this problem by proposing a procedure that checks in polynomial time the existence of a weak combined transition satisfying the step condition of the bisimulation.

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arXiv ID1205.0376 (version 2)
Pith IDFDFQVRZL, Pith's permanent record of this paper and its review
CitationAndrea Turrini, Holger Hermanns. "Deciding Probabilistic Automata Weak Bisimulation in Polynomial Time." arXiv:1205.0376 (2012). https://pith.science/paper/FDFQVRZL
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,645 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.16 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.57 · compares with prior results 0.20 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Deciding in an efficient way weak probabilistic bisimulation in the context of Probabilistic Automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the existence of a weak combined transition satisfying the step condition of the bisimulation. We also present several extensions of weak combined transitions, such as hyper-transitions and the new concepts of allowed weak combined and hyper-transitions and of equivalence matching, that turn out to be verifiable in polynomial time as well. These results set the ground for the development of more effective compositional analysis algorithms for probabilistic systems.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Deciding in an efficient way weak probabilistic bisimulation in the context of Probabilistic Automata is an open problem for about a decade. gap 0.77 0.04 0.04 asserted 1.00
s1 In this work we close this problem by proposing a procedure that checks in polynomial time the existence of a weak combined transition satisfying the step condition of the bisimulation. contribution 0.91 0.96 0.91 asserted 1.00
s2 We also present several extensions of weak combined transitions, such as hyper-transitions and the new concepts of allowed weak combined and hyper-transitions and of equivalence matching, that turn out to be verifiable in polynomial time as well. contribution 0.94 0.94 0.13 asserted 1.00
s3 These results set the ground for the development of more effective compositional analysis algorithms for probabilistic systems. interpretation 0.85 0.35 0.11 asserted 0.78

What kind of paper the classifier reports this is: method or tool 0.85 · evidence from proof or derivation 0.98.

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  • P abstract
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  • S sections
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  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Deciding in an efficient way weak probabilistic bisimulation in the context of Probabilistic Automata is an open problem for about a decade. In this work we close this problem by proposing a procedure that checks in polynomial time the existence of a weak combined transition satisfying the step condition of the bisimulation. We also present several extensions of weak combined transitions, such as hyper-transitions and the new concepts of allowed weak combined and hyper-transitions and of equivalence matching, that turn out to be verifiable in polynomial time as well. These results set the ground for the development of more effective compositional analysis algorithms for probabilistic systems.

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1 arXiv paper cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Compares with it 1 paper
  • Even if the problem of deciding naïve weak bisimulation as recently been shown to be solvable in polynomial time [ref] , the decision problem for weak bisimulation remains exponential as finding vanishing representations involves all dirac determinate schedulers (which are exponentially many, as has been shown in [ref] ).

    Markov Automata: Deciding Weak Bisimulation by means of non-naively Vanishing States · A partition refinement algorithm · 0.89

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