Multi-Sequential Word Relations

Rational relations are binary relations of finite words that are realised by non-deterministic finite state transducers (NFT). A multi-sequential relation is a rational relation which is equal to a finite union of (graphs) of partial sequential functions, i.e. functions realised by input-deterministic transducers. The particular case of multi-sequential functions was studied by Choffrut and Schützenberger who proved that given a rational function (as a transducer), it is decidable whether it is multi-sequential. Their procedure is based on an effective characterisation of unambiguous transducers that do not define multi-sequential functions, that we call the fork property. In this paper, we show that the fork property also characterises the class of transducers that do not define multi-sequential relations. Moreover, we prove that the fork property can be decided in PTime. This leads to a PTime procedure which, given a transducer, decides whether it defines a multi-sequential relation.

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USING AN EXTENSIONS OF CTL* FOR SPECIFICATION AND VERIFICATION OF SEQUENTIAL REACTIVE SYSTEMS

System Informatics ◽

10.31144/si.2307-6410.2020.n17.p21-32 ◽

2020 ◽

Author(s):

Anton Romanovich Gnatenko ◽

◽

Vladimir Anatolyevoch Zakharov ◽

Keyword(s):

Model Checking ◽

Formal Model ◽

Reactive Systems ◽

Expressive Power ◽

Binary Relations ◽

Temporal Logics ◽

Finite State Transducers ◽

Control Signals ◽

Data Control ◽

Finite State

Sequential reactive systems such as controllers, device drivers, computer interpreters operate with two data streams and transform input streams of data (control signals, instructions) into output streams of control signals (instructions, data). Finite state transducers are widely used as an adequate formal model for information processing systems of this kind. Since runs of transducers develop over time, temporal logics, obviously, could be used as both simple and expressive formalism for specifying the behavior of sequential reactive systems. However, the conventional applied temporal logics (LTL, CTL) do not suit this purpose well, since their formulae are interpreted over omega-languages, whereas the behavior of transducers are represented by binary relations on infinite sequences, i.e. omega-transductions. To provide temporal logic with the ability to take into account this general feature of the behavior of reactive systems, we introduced new extensions of this logic. Two distinguished features characterize these extension: 1) temporal operators are parameterized by sets of streams (languages) admissible for input, and 2) sets (languages) of expected output streams are used as basic predicates. In the previous series of works we studied the expressive power and the model checking problem for Reg-LTL and Reg-CTL which are such extensions of LTL and CTL where the languages mentioned above are regular ones. We discovered that such an extension of temporal logics increases their expressive capability though retains the decidability of the model checking problem. Our next step in the systematic study of expressive and algorithmic properties of new extensions temporal logics is the analysis of the model checking problem for finite state transducers against Reg-CTL* formulae. In this paper we develop a model checking algorithm for Reg-CTL* and show that this problem is in ExpSpace.

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Composition of weighted finite transducers in MapReduce

Journal Of Big Data ◽

10.1186/s40537-020-00397-4 ◽

2021 ◽

Vol 8 (1) ◽

Author(s):

Bilal Elghadyry ◽

Faissal Ouardi ◽

Sébastien Verel

Keyword(s):

Speech Processing ◽

Large Scale ◽

Large Scale Data ◽

Finite State Transducers ◽

Wide Range ◽

Finite State ◽

Common Operation ◽

Efficient Representation ◽

Weighted Finite State Transducers ◽

Np Hardness

AbstractWeighted finite-state transducers have been shown to be a general and efficient representation in many applications such as text and speech processing, computational biology, and machine learning. The composition of weighted finite-state transducers constitutes a fundamental and common operation between these applications. The NP-hardness of the composition computation problem presents a challenge that leads us to devise efficient algorithms on a large scale when considering more than two transducers. This paper describes a parallel computation of weighted finite transducers composition in MapReduce framework. To the best of our knowledge, this paper is the first to tackle this task using MapReduce methods. First, we analyze the communication cost of this problem using Afrati et al. model. Then, we propose three MapReduce methods based respectively on input alphabet mapping, state mapping, and hybrid mapping. Finally, intensive experiments on a wide range of weighted finite-state transducers are conducted to compare the proposed methods and show their efficiency for large-scale data.

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FINITELY SUBSEQUENTIAL TRANSDUCERS

International Journal of Foundations of Computer Science ◽

10.1142/s0129054103002126 ◽

2003 ◽

Vol 14 (06) ◽

pp. 983-994 ◽

Cited By ~ 9

Author(s):

CYRIL ALLAUZEN ◽

MEHRYAR MOHRI

Keyword(s):

Speech Recognition ◽

Finite Number ◽

Efficient Algorithm ◽

Experimental Results ◽

Theoretical Formulation ◽

Large Vocabulary ◽

Finite State Transducers ◽

Finite State ◽

Large Vocabulary Speech Recognition

Finitely subsequential transducers are efficient finite-state transducers with a finite number of final outputs and are used in a variety of applications. Not all transducers admit equivalent finitely subsequential transducers however. We briefly describe an existing generalized determinization algorithm for finitely subsequential transducers and give the first characterization of finitely subsequentiable transducers, transducers that admit equivalent finitely subsequential transducers. Our characterization shows the existence of an efficient algorithm for testing finite subsequentiability. We have fully implemented the generalized determinization algorithm and the algorithm for testing finite subsequentiability. We report experimental results showing that these algorithms are practical in large-vocabulary speech recognition applications. The theoretical formulation of our results is the equivalence of the following three properties for finite-state transducers: determinizability in the sense of the generalized algorithm, finite subsequentiability, and the twins property.

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