We give a new and simple proof of a key lemma on the rank of a matrix in Leung's paper [3], where he showed there exists a family of nondeterministic nite automata fAng, with n states and exponential ambiguity, such that any smallest equivalent polynomially ambiguous nite automaton has 2 1 states. Keyword: nondeterministic automata, ambiguity, automata theory.

The parity acceptance condition for ω-regular languages is a special case of the Rabin and Streett acceptance conditions. While the parity acceptance condition is as expressive as the richer conditions, in both the deterministic and nondeterministic settings, Rabin and Streett automata are more succinct, and their translation to parity automata may blow-up the state space. The appealing propert...

Every regular expression can be transformed into a Nondeterministic Finite Automaton (NFA) with or without  transitions. A well known algorithm called subset construction technique is used for conversion of NFA into DFA. In this paper, initially, the construction of the position automaton is given for the same. Also, the algorithm to convert this Position Automaton into DFA using subset constr...

Checking for language containment between nondeterministic ω-automata is a central task in automata-based hierarchical verification. We present a symbolic procedure for language containment checking between two Büchi automata. Our algorithm avoids determinization by intersecting the implementation automaton with the complement of the specification automaton as an alternating automaton. We prese...

A finite automaton can be either deterministic (DFA) or nondeterministic (NFA). An automaton-based task is in general more efficient when performed with a DFA rather than an NFA. For any NFA there equivalent that generated by the classical Subset Construction algorithm. When, however, large may transformed into series of actions operating directly on NFA, unnecessarily expensive computation, as...

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...

Glushkov algorithm computes a nondeterministic nite automaton without-transition and with n + 1 states from a simple regular expression having n occurrences of letters. The aim of this paper is to give a set of necessary and suucient conditions characterizing this automaton. Our characterization theorem is formulated in terms of directed graphs. Moreover these conditions allow us to produce an ...

We solve the longstanding open problems of the blowup involved in the translations (when possible) of a nondeterministic Büchi word automaton (NBW) to a nondeterministic co-Büchi word automaton (NCW) and to a deterministic co-Büchi word automaton (DCW). For the NBW to NCW translation, the currently known upper bound is 2 logn) and the lower bound is 1.5n. We improve the upper bound to n2 and de...

We investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent oneway and two-way deterministic finite automata, from a descriptional complexity point of view. We prove that for each one-way nondeterministic automaton with n states there exist Parikh equivalent one-way and two-way deterministic automata with e √ n·lnn) and p(n) states,...

We introduce a new formal computational model designed for studying the information transfer among the generations of offspring-producing evolving machines — so-called autopoietic automata. These can be seen as nondeterministic finite state transducers whose “program” can become a subject of their own processing. An autopoietic automaton can algorithmically generate an offspring controlled by a...