General automata are considered with respect to normal-ization over semirings. Possibilistic automata are deened as normal pessimistic fuzzy automata. Possibilistic automata are analogous to stochas-tic automata where stochastic (+=) semirings are replaced by possi-bilistic (_=^) semirings; but where stochastic automata must be normal, fuzzy automata may be (resulting in possibilistic automata)...

Liveness properties of on-going reactive systems assert that something good will happen eventually. In satisfying liveness properties, there is no bound on the “wait time”, namely the time that may elapse until an eventuality is fulfilled. The traditional “unbounded” semantics of liveness properties nicely corresponds to the classical semantics of automata on infinite objects. Indeed, acceptanc...

Two variants of pebble tree-walking automata on trees are considered that were introduced in the literature. It is shown that for each number of pebbles, the two models have the same expressive power both in the deterministic case and in the nondeterministic case. Furthermore, nondeterministic (resp. deterministic) treewalking automata with n+ 1 pebbles can recognize more languages than those w...

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...

Different types of nondeterministic automata on infinite words differ in their succinctness and in the complexity for their nonemptiness problem. A simple translation of a parity automaton to an equivalent Büchi automaton is quadratic: a parity automaton with n states, m transitions, and index k may result in a Büchi automaton of size O((n + m)k). The best known algorithm for the nonemptiness p...

We define a structurally unambiguous finite automaton (SUFA) to be a nondeterministic finite automaton (NFA) with one starting state q0 such that for all input strings w and for any state q, there is at most one path from q0 to q that consumes w. The definition of SUFA differs from the usual definition of an unambiguous finite automaton (UFA) in that the new definition is defined in terms of th...

We extend Antimirov’s partial derivatives from regular expressions to μ-regular expressions that describe context-free languages. We prove the correctness of partial derivatives as well as the finiteness of the set of iterated partial derivatives. The latter are used as pushdown symbols in our construction of a nondeterministic pushdown automaton, which generalizes Antimirov’s NFA construction.

We investigate the complexity of deciding whether a given regular language can be defined with a deterministic regular expression. Our main technical result shows that the problem is PSPACE-complete if the input language is represented as a regular expression or nondeterministic finite automaton. The problem becomes EXPSPACE-complete if the language is represented as a regular expression with c...

Glushkov’s algorithm builds an ε-free nondeterministic automaton from a given regular expression. In the worst case, its number of states is linear and its number of transitions is quadratic in the size of the expression. We show in this paper that in average, the number of transitions is linear.

There are several types of finite automata on infinite words, differing in their acceptance conditions. As each type has its own advantages, there is an extensive research on the size blowup involved in translating one automaton type to another. Of special interest is the Muller type, providing the most detailed acceptance condition. It turns out that there is inconsistency and incompleteness i...