Category of L-valued Multiset Automata and Brzozowski’s Algorithm

Abstract

The purpose of this work is to use the concepts of reachability and coreachability maps to provide a solution of a well-known characterization for [Formula: see text]-valued multiset regular languages. In between, we associate two deterministic [Formula: see text]-valued multiset automata with a given deterministic [Formula: see text]-valued multiset automaton (DLMA) and show that the reachability and coreachability maps of the given DLMA turn out to be morphisms in the category of deterministic [Formula: see text]-valued multiset automata.

Fuzzy Multiset Finite Automata: Some Algebraic and Lattice Theoretic Characterizations

“…The FMRG, FMFA and FMLs have been studied by Wang, Yin and Gu [37] and by Sharma, Syropoulos and Tiwari [42], Sharma, Gautam, Tiwari and Bhattacherjee [97]. The category of lattice-valued FMFA and minimal realization of L-valued multiset languages by Brozozowski's algorithm were discussed by Pal and Tiwari [44], while the minimal realization of FMLs in the general categorical framework was recently studied by Yadav and Tiwari [47]. The most recent articles dealing with FMFA and showing the importance of multiset theory in theoretical computer science are due to Dhingra et.…”

“…It is worth to mention here that the multiset automata and fuzzy multiset automata are generalized versions of classical and fuzzy automata whose inputs are multisets (bags), in these models of computations processing of a symbol does not follow any strict order, i.e., any symbol from'input bag' can be utilized without affecting the output. Furthermore, Wang and Li [43] studied the lattice-valued FMFA minimization problem and Pal and Tiwari [44] considered Brazozowaski's algorithm and the categorical approaches for the same, while Singh, Dubey and Perfilieva [45] discussed quotient structures of FMFA, and Gautam [46] studied l-valued FMFA and l-valued FMLs. Recently Yadav and Tiwari [47] provide a general categorical framework of minimal realization of fuzzy multiset languages.…”

On Quotient Structures of Fuzzy Multiset Finite Automata

“…The minimization of fuzzy multiset finite automata with membership value in a distributive lattice were studied by Wang et al [22] and a simplified version of fuzzy multiset automata has been discussed in [20]. Recently, Pal et al [12] applied the Brzozowski's algorithm to study the minimal realization of an L-valued multiset language. However, the study of quotient structure based fuzzy multiset finite automata is still missing.…”