Containment and Equivalence of Weighted Automata: Probabilistic and Max-Plus Cases

Daviaud, Laure

doi:10.1007/978-3-030-40608-0_2

Cited by 2 publications

(1 citation statement)

References 42 publications

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“…For WFAs over an ordered semiring this is the question of determining whether the function computed by one WFA is less than or equal to the function computed by the other WFA (with respect to the pointwise ordering of functions). The complexity and decidability of these decision problems depend upon the type of WFAs under consideration, i.e., it depends both on the determinism of the automata and the underlying semiring (for more information we refer to [17,18,33]). In cases where the containment or equivalence problem is undecidable or computationally hard, the question naturally arises as to whether it is possible to efficiently determine "something" that implies containment or equivalence.…”

Section: Introductionmentioning

confidence: 99%

Bisimulations for weighted finite automata over semirings

Ćirić

2022

Preprint

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Simulation and bisimulation relations are powerful tools used in many areas of computer science to match moves and compare the behaviour of various computational systems, such as labelled transition systems and automata, as well as to reduce the number of states of these systems. By moving from traditional boolean systems to quantitative ones, a need arise for both simulations and bisimulations to be quantitative, to be modeled with matrices whose entries should provide some quantitative measure of the relationship between the states of the considered systems. In the present paper, we introduce several types of quantitative simulations and bisimulations for weighted finite automata over semirings. For weighted finite automata over positive semirings two tipes of simulations and two types of bisimulations are defined as solutions to particular systems of matrix inequations, while for weighted finite automata over arbitrary semirings four types of bisimulations are defined as solutions to particular systems of matrix equations. Both types of simulations are proven to ensure the containment, while all types of bisimulations are proven to ensure the equivalence of weighted finite automata. Certain general properties of simulations and bisimulations are also proved.

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Section: Introductionmentioning

confidence: 99%

Bisimulations for weighted finite automata over semirings

Ćirić

2022

Preprint

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Simultaneous Method for Solving Certain Systems of Matrix Equations with Two Unknowns

Stanimirović,

Ćirić,

Mourtas

et al. 2024

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Quantitative bisimulations between weighted finite automata are defined as solutions of certain systems of matrix-vector inequalities and equations. In the context of fuzzy automata and max-plus automata, testing the existence of bisimulations and their computing are performed through a sequence of matrices that is built member by member, whereby the next member of the sequence is obtained by solving a particular system of linear matrix-vector inequalities and equations in which the previously computed member appears. By modifying the systems that define bisimulations, systems of matrix-vector inequalities and equations with k unknowns are obtained. Solutions of such systems, in the case of existence, witness to the existence of a certain type of partial equivalence, where it is not required that the word functions computed by two WFAs match on all input words, but only on all input words whose lengths do not exceed k. Solutions of these new systems represent finite sequences of matrices which, in the context of fuzzy automata and max-plus automata, are also computed sequentially, member by member. Here we deal with those systems in the context of WFAs over the field of real numbers and propose a different approach, where all members of the sequence are computed simultaneously. More precisely, we apply a simultaneous approach in solving the corresponding systems of matrix-vector equations with two unknowns. Zeroing neural network (ZNN) neuro-dynamical systems for approximating solutions of heterotypic bisimulations are proposed. Numerical simulations are performed for various random initial states and comparison with the Matlab, linear programming solver linprog, and the pseudoinverse solution generated by the standard function pinv is given.

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Containment and Equivalence of Weighted Automata: Probabilistic and Max-Plus Cases

Cited by 2 publications

References 42 publications

Bisimulations for weighted finite automata over semirings

Bisimulations for weighted finite automata over semirings

Simultaneous Method for Solving Certain Systems of Matrix Equations with Two Unknowns

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