We address the concrete problem of verifying graph properties expressed in Monadic Second Order (MSO) logic. It is well-known that the model-checking problem for MSO logic on graphs is fixed-parameter tractable (FPT) [Cou09, Chap 6] with respect to tree-width and cliquewidth. The proof uses tree-decompositions (for tree-width as parameter) and clique-decompositions (for clique-width as paramete...

Studies of computational complementarity properties in finite state interactive automata may shed light on the nature of both quantum and classical computation. But, complementarity is difficult to test even for small-size automata. This paper introduces the concept of an observation graph of an automaton which is used as the main tool for the design of an algorithm which tests, in a uniform ma...

We consider a deterministic finite automaton which accepts all subsequences of a set of texts, called subsequence automaton. We show an online algorithm for constructing subsequence automaton for a set of texts. It runs in O(|Σ|m) time using O(|Σ|m) space, where m is the number of states of the subsequence automaton, and |Σ| is the size of alphabet. For k texts of length n, since m = O(n), it r...

Techniques from linear algebra are used to study the synchronization problem in automata theory. Let A = (Q, X) be a finite automaton. Each word m in X∗ defines a map from Q to Q ; the rank of m in A is the integer Card{qm | q ∈ Q}. A word of rank 1 maps all states onto a unique state. Such a word is called a synchronizing word (if such a word exists the automaton itself is called a synchronizi...

It is shown that any context-sensitive language can be generated by a tree controlled grammar whose control language is accepted by a deterministic finite automaton with at most 5 states.

In a similar way to DNA hybridization, antibodies which specifically recognize peptide sequences can be used for calculation [3,4]. In [4] the concept of peptide computing via peptide-antibody interaction is introduced and an algorithm to solve the satisfiability problem is given. In [3], (1) it is proved that peptide computing is computationally complete and (2) a method to solve two well-know...

On every n-long input, every two-way finite automaton (fa) can reverse its input head O(n) times before halting. A fawith few reversals is an automaton where this number is only o(n). For every h, we exhibit a language that can be recognized by an h-state nondeterministic fa with few reversals, but requires Ω(2) states on every deterministic fa with few reversals.

For a givenweighted finite automaton over a strong bimonoid we construct its reducedNerode automaton, which is crisp-deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics.We show that the reducedNerode automaton is even smaller than theNerode automaton, which was previously used in determinization related to this semantics. We determine ne...

We show that every regular language defines a unique nondeterministic finite automaton (NFA), which we call “átomaton”, whose states are the “atoms” of the language, that is, non-empty intersections of complemented or uncomplemented left quotients of the language. We describe methods of constructing the átomaton, and prove that it is isomorphic to the normal automaton of Sengoku, and to an auto...

it is essential to use statistical models and theoretical analysis of the data for preparing comprehensive geological and seismic hazard mapping. a cellular automaton consists of an array of cells, each one of which has a finite number of possible states, together with a rule for updating all cells simultaneously based only on the states of neighboring cells. in the present paper, ising cellula...