The synthesis of reactive systems requires the solution of two-player games on graphs with ω-regular objectives. When the objective is specified by a linear temporal logic formula or nondeterministic Büchi automaton, then previous algorithms for solving the game require the construction of an equivalent deterministic automaton. However, determinization for automata on infinite words is extremel...

It is well known, and easy to see, that not each nondeterministic Büchi automaton on in nite words can be simulated by a nondeterministic co-Büchi automaton. We show that in the cases when such a simulation is possible, the number of states needed for it can grow nonlinearly. More precisely, we show a sequence of as we believe, simple and elegant languages which witness the existence of a nonde...

The minimization of nondeterministic automata without initial states (developed within a game-theoretic framework in Calude, Calude, Khoussainov [3]) is presented in terms of bisimulations; the minimal automaton is unique up to an isomorphism in case of reversible automata. We also prove that there exists an infinite class of (strongly connected) nondeterministic automata each of which is not b...

Okhotin [9] showed an exponential trade-off in the conversion from nondeterministic unary finite automata to unambiguous nondeterministic unary finite automata. In this paper, we consider the trade-off in the case of unary symmetric difference finite automata to finitely ambiguous unary symmetric difference finite automata. Surprisingly, the trade-off is linear in the number of states of the fi...

We prove that every two-way nondeterministic finite automaton with n states has an equivalent one-way nondeterministic finite automaton with at most 2n n+1 states. We also show this bound is exact.

The nonemptiness problem for nondeterministic automata on infinite words can be reduced to a sequence of reachability queries. The length of a shortest witness to the nonemptiness is then polynomial in the automaton. Nonemptiness algorithms for alternating automata translate them to nondeterministic automata. The exponential blow-up that the translation involves is justified by lower bounds for...

For each positive integer r ≥ 1, a nondeterministic machine M is r path-bounded if for any input word x, there are r computation paths of M on x. This paper investigates the accepting powers of pathbounded one-way (simple) multihead nondeterministic finite automata. It is shown that for each k ≥ 2 and r ≥ 1, there is a language accepted by an (r+1) path-bounded one-way nondeterministic k head f...

Okhotin showed an exponential trade-off in the conversion from nondeterministic unary automata to unambiguous nondeterministic unary automata. We show that the trade-off in the case of unary symmetric difference automata to finitely (structurally) ambiguous unary symmetric difference automata is linear with constant 1 in the number of states. In particular, for every n-state unary nondeterminis...

Modeling the morphological structure of natural languages in terms of a nondeterministic finite-state automaton is shown to be inadequate in its handling of some common natural language phenomena. We show that a two-tape nondeterministic automaton is capable of handling these phenomena. The modeling is improved by the specification of a new type of automaton, the preset two-head automaton, whic...

Trees can be conveniently compressed with linear straight-line context-free tree grammars. Such grammars generalize straight-line context-free string grammars which are widely used in the development of algorithms that execute directly on compressed structures (without prior decompression). It is shown that every linear straight-line context-free tree grammar can be transformed in polynomial ti...