Automata theory plays a key role in computational theory as many computational problems can be solved with its help. Formal grammar is a special type of automata designed for linguistic purposes. Formal grammar generates formal languages. Rough grammar and rough languages were introduced to incorporate the imprecision of real languages in formal languages. These languages have limitations on un...

Classical automata theory cannot deal with the system uncertainty. To deal with the system uncertainty the concept of fuzzy finite automata was proposed. Fuzzy automata can be used in diverse applications such as fault detection, pattern matching, measuring the fuzziness between strings, description of natural languages, neural network, lexical analysis, image processing, scheduling problem and...

[2] Karsten Lehmann and Rafael Peñaloza. The complexity of computing the behaviour of lattice automata on infinite trees. On the decidability status of fuzzy ALC with general concept inclusions. [4] Stefan Borgwardt and Rafael Peñaloza. Consistency reasoning in lattice-based fuzzy description logics. Context-dependent views to axioms and consequences of semantic web ontologies. Classifying soft...

Classical automata theory can not deal with uncertainty. To deal with uncertainty in system modeling, fuzzy automata come into the existence. Fuzzy automaton depends on membership value. For finding the membership degree of strings in fuzzy automata, the concept of max – min automaton and min – max automaton can be used. Many researchers have used the concept of max – min automaton for finding ...

The model we consider are stateless counter machines which mix the features of one-head counter machines and special two-head Watson-Crick automata (WK-automata). These biologically motivated machines have reading heads that read the input starting from the two extremes. The reading process is finished when the heads meet. The machine is realtime or non-realtime depending on whether the heads a...

Fuzzy Cellular Automata (FCA) are special couple map lattices that generalize Boolean cellular automata by allowing continuous values for the cell states. The local transition rule of a FCA is the “fuzzification" of the disjunctive normal form that describes the local function of the corresponding Boolean cellular automata. Recently there has been some interest in elementary Fuzzy cellular auto...

Some uniform categorical theoretical treatment of automata and lattice-valued fuzzy automata using quantale theory is studied in this paper. First, L-relational sheaves on a monoidM andQ-enriched categories are introduced for quantales L andQ, the equivalence of the corresponding categories are proved next. Then lattice-valued (fuzzy) automata are described by Q-enriched categories. In fact, la...

Simulations and bisimulations between two fuzzy automata over a complete residuated lattice were defined by Ćirić et al. (2012) [7], [8] as relations the sets of states automata. However, they act crisp relationship In particular, if there exists (forward) bisimulation automata, then languages recognized them are crisply equal. Approximate simulations introduced Stanimirović (2022) [36] aim at ...