In 2001, van Leeuwen and Wiedermann [1] have defined evolving interactive systems, in particular sequences of interactive finite automata with global states, to model infinite computations on an ever changing machine or system of machines. Modern computation does not just happen on an individual machine for a fixed time, but it goes on forever over an unbounded number of software and hardware c...

We consider weighted finite automata over strong bimonoids, where these weight structures can be considered as semirings which might lack distributivity. Then, in general, the well-known run semantics, initial algebra semantics, and transition semantics of an automaton are different. We prove an algebraic characterization for the initial algebra semantics in terms of stable finitely generated s...

Model checking is one of the most practical techniques of automatic formal verification to ensure the correctness of design specifications. The problem that the number of states can become too large for model-checking real-time system is known as the state-space explosion problem. An optimization definition of clock equivalence, the key to model checking real-time, was described for model check...

Cover automata were introduced in [1] as an efficient representation of finite languages. In [1], an algorithm was given to transform a DFA that accepts a finite language to a minimal deterministic finite cover automaton (DFCA) with the time complexity O(n), where n is the number of states of the given DFA. In this paper, we introduce a new efficient transformation algorithm with the time compl...

A biomolecular, programmable 3-symbol-3-state finite automaton is reported. This automaton computes autonomously with all of its components, including hardware, software, input, and output being biomolecules mixed together in solution. The hardware consisted of two enzymes: an endonuclease, BbvI, and T4 DNA ligase. The software (transition rules represented by transition molecules) and the inpu...

We investigate the ambiguity behavior of finite automata in connection with their inner structure. We show that the degree of ambiguity of a finitely ambiguous nondeterministic finite automaton (NFA) with n states is at most 5”“.n”. There is a simple criterion which characterizes the infinite degree of ambiguity of an NFA, and which is decidable in polynomial time. The degree of growth of the a...

in this note, by considering the notions of the intuitionistic general l-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{l}$, there exists a minimal intuitionistic general l-fuzzy automaton recognizing $mathcal{l}$.we prove that the minimal intuitionistic general l-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, be...

Abstract—Deterministic Finite Automatons (DFAs) and Nondeterministic Finite Automatons (NFAs) are two typical automatons used in the Network Intrusion Detection System (NIDS). Although they both perform regular expression matching, they have quite different performance and memory usage properties. DFAs provide fast and deterministic matching performance but suffer from the well-known state expl...

The only presently known normal form for a regular language L ∈ Reg is its Minimal Deterministic Automaton MDA(L). We show that a regular language is also characterized by a finite dimension dim(L), which is always smaller than the number |MDA(L)| of states, and often exponentially so. The dimension is also the minimal number of states of all Nondeterministic Xor Automaton (NXA) which accept th...