Mathematical models in classical computation, automata have been an important area in theoretical computer science. It started from a seminal paper of Kleene, and within a few years developed into a rich mathematical research topic. From the very beginning finite automata constituted a core of computer science. Part of the reason is that they capture something very fundamental as is witnessed b...

Let C be a oneor two-sided Kazhdan–Lusztig cell in a Coxeter group (W,S), and let Reduced(C) be the set of reduced expressions of all w ∈ C, regarded as a language over the alphabet S. Casselman has conjectured that Reduced(C) is regular. In this paper we give a conjectural description of the cells when W is the group corresponding to a hyperbolic polygon, and show that our conjectures imply Ca...

In this paper, we introduce oracle (finite) automata that are finite/Buchi automata augmented with oracles in some classes of formal languages. We present some testability results for the emptiness problem of oracle automata associated with various classes of oracles. Moreover, we show that some important verification problems (such as reachability, safety, LTL model-checking, etc.) for oracle ...

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...

The semantic automata framework, developed originally in the 1980s, provides computational interpretations of generalized quantifiers. While recent experimental results have associated structural features of these automata with neuroanatomical demands in processing sentences with quantifiers, the theoretical framework has remained largely unexplored. In this paper, after presenting some classic...

A novel approach to automata-based modeling for spatial systems is described: geographic automata and Geographic Automata Systems. We detail a framework that takes advantage of the formalism of automata theory and GI Science to unite cellular automata and multi-agent systems techniques, and provides a spatial approach to bottom-up modeling of complex geographic systems that are comprised of inf...

We de ne robust timed automata, which are timed automata that accept all trajectories \robustly": if a robust timed automaton accepts a trajectory, then it must accept neighboring trajectories also; and if a robust timed automaton rejects a trajectory, then it must reject neighboring trajectories also. We show that the emptiness problem for robust timed automata is still decidable, by modifying...

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...