A Polynomial-Time Algorithm for the Equivalence of Probabilistic Automata

Tzeng, Wen-Guey

doi:10.1137/0221017

Cited by 117 publications

(155 citation statements)

References 3 publications

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“…The complexity of the algorithm is O(nm), where n is the number of states of the two automata being compared and m is the total number of labelled transitions. Tzeng [21] states the complexity of his algorithm as O(|Σ| · n 4 ); the same complexity bound is likewise claimed by [5,10] for variants of Tzeng's procedure. Here we observe that the procedure can be implemented with complexity O(|Σ| · n 3 ), which is still slower than the randomised algorithm.…”

supporting

confidence: 52%

“…Instead we have managed to speed up the algorithms of [21] and [10] from O(|Σ| · n 4 ) to O(|Σ| · n 3 ) by efficient bookkeeping of the involved vector spaces. Whereas [7] suggests to maintain an LU decomposition to represent the involved vector spaces, we prefer a QR decomposition for stability reasons.…”

Section: Deterministic Algorithmsmentioning

confidence: 99%

“…Whereas [7] suggests to maintain an LU decomposition to represent the involved vector spaces, we prefer a QR decomposition for stability reasons. We have implemented two versions of a deterministic algorithm for equivalence checking: a forward version (related to [21]) and a backward version (related to [10]). In the following we describe the backward algorithm; the forward version is obtained essentially by transposing the transition matrices and exchanging initial and final states.…”

Section: Deterministic Algorithmsmentioning

confidence: 99%

“…In fact this problem can be decided in polynomial time. For instance, Tzeng's algorithm [21] explores the tree of possible input words and computes for each word w in the tree and for both automata the distribution of states after having read w. The tree is suitably pruned by eliminating nodes whose associated state distributions are linearly dependent on previously discovered state distributions. Tzeng's procedure has a runtime of O(|Σ| · n 4 ).…”

Section: From Now On We Fix Automatamentioning

confidence: 99%

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Language Equivalence for Probabilistic Automata

Kiefer

Murawski

Ouaknine

et al. 2011

Computer Aided Verification

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Abstract. In this paper, we propose a new randomised algorithm for deciding language equivalence for probabilistic automata. This algorithm is based on polynomial identity testing and thus returns an answer with an error probability that can be made arbitrarily small. We implemented our algorithm, as well as deterministic algorithms of Tzeng and Doyen et al., optimised for running time whilst adequately handling issues of numerical stability. We conducted extensive benchmarking experiments, including the verification of randomised anonymity protocols, the outcome of which establishes that the randomised algorithm significantly outperforms the deterministic ones in a majority of our test cases. Finally, we also provide fine-grained analytical bounds on the complexity of these algorithms, accounting for the differences in performance.

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supporting

confidence: 52%

Section: Deterministic Algorithmsmentioning

confidence: 99%

Section: Deterministic Algorithmsmentioning

confidence: 99%

Section: From Now On We Fix Automatamentioning

confidence: 99%

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Language Equivalence for Probabilistic Automata

Kiefer

Murawski

Ouaknine

et al. 2011

Computer Aided Verification

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“…For instance, functional equivalence is decidable in polynomial time [13,14], and even faster with randomised algorithms, which led to applications in software verification [9].…”

Section: Introductionmentioning

confidence: 99%

Two Recursively Inseparable Problems for Probabilistic Automata

Fijalkow

Gimbert

Horn

et al. 2014

Mathematical Foundations of Computer Science 2014

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Abstract. This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact values of the probabilities are not. A numberless probabilistic automaton can be instantiated into a probabilistic automaton by specifying the exact values of the non-zero probabilistic transitions. We show that the two following properties of numberless probabilistic automata are recursively inseparable:• all instances of the numberless automaton have value 1, • no instance of the numberless automaton has value 1.

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IEEE Transactions on Pattern Analysis and Machine Intelligence

Fu¹

2004

Encyclopedia of Statistical Sciences

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Probabilistic finite-state machines are used today in a variety of areas in pattern recognition, or in fields to which pattern recognition is linked: computational linguistics, machine learning, time series analysis, circuit testing, computational biology, speech recognition, and machine translation are some of them. In Part I of this paper, we survey these generative objects and study their definitions and properties. In Part II, we will study the relation of probabilistic finite-state automata with other well-known devices that generate strings as hidden Markov models and n-grams and provide theorems, algorithms, and properties that represent a current state of the art of these objects.

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A Polynomial-Time Algorithm for the Equivalence of Probabilistic Automata

Cited by 117 publications

References 3 publications

Language Equivalence for Probabilistic Automata

Language Equivalence for Probabilistic Automata

Two Recursively Inseparable Problems for Probabilistic Automata

IEEE Transactions on Pattern Analysis and Machine Intelligence

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