A Finite Field Framework for Modeling, Analysis and Control of Finite State Automata

A Finite Field Framework for Modeling, Analysis and Control of Finite State Automata

ing from the latter exemplary viewpoint, in general we obtain a multilinear transition function f : F2 ×F2 ×F2 → F2 f (x[k+1],x[k],u[k]) = 0 = ∑ S1∈2In ∑ S2∈2In ∑ S3∈2Im δS1,S2,S3 ( ∏ j∈S1 x j[k+1] )( ∏ l∈S2 xl[k] )( ∏ m∈S3 um[k] ) , (21) with x ∈ F2 and u ∈ F2 , where the sets In = {1,2, . . . ,n}, Im = {1,2, . . . ,m} are index sets, 2In denotes the (possibly empty) power set of In and δS1,S2...

Modeling and analyzing finite state automata in the finite field F2

Cycle Analysis for Deterministic Finite State Automata

A method for the determination of all cycles of deterministic finite state automata is presented. Using a finite field description GF(2) these automata are shown to correspond to multilinear state equations. Basic results from feedback shift register theory are recalled and developed towards a complete analysis tool for affine-linear automata. The multilinear case is reduced to the affine-linea...

Optimal supervisory control of finite state automata

This paper presents optimal supervisory control of dynamical systems that can be represented by deterministic finite state automaton (DFSA) models. The performance index for the optimal policy is obtained by combining a measure of the supervised plant language with (possible) penalty on disabling of controllable events. The signed real measure quantifies the behaviour of controlled sublanguages...

Automatic learning of finite state automata for pronunciation modeling

The great variability of word pronunciations in spontaneous speech is one of the reasons for the low performance of the present speech recognition systems. The generation of dictionaries that take into account this variability can increase the robustness of such systems. A word pronunciation is a possible phone sequence that can appear in a real utterance, and represents a possible acoustic rea...