We show that for all n and α such that 1 ≤ n ≤ α ≤ 2 there is a minimal n-state nondeterministic finite automaton whose equivalent minimal deterministic automaton has exactly α states.

The deterministic membership problem for timed automata asks whether the language given by a nondeterministic automaton can be recognised automaton. An analogous stated in setting of register automata. We draw complete decidability/complexity landscape problem, both and For automata, we prove that is decidable when input one-register (possibly with epsilon transitions) number registers output f...

Abstract Automata operating on infinite objects feature prominently in the theory of modal $$\mu $$ -calculus. One such application concerns tableau games introduced by Niwiński & Walukiewicz, which winning condition for plays can be naturally checked a nondeterministic parity stream automaton. Inspired work Jungteerapanich and Stirling we show how determinization constructions this automat...

It is a well-known fact that a nondeterministic automaton can be transformed into an equivalent deterministic automaton via the powerset construction. From a categorical perspective this construction is the right adjoint to the inclusion functor from the category of deterministic automata to the category of nondeterministic automata. This is in fact an adjunction between two categories of coalg...

We revisit the problem of deciding whether a given string is uniquely decodable from its bigram counts by means of a finite automaton. An efficient algorithm for constructing a polynomial-size nondeterministic finite automaton that decides unique decodability is given. Conversely, we show that the minimum deterministic finite automaton for deciding unique decodability has at least exponentially...

We investigate the nondeterministic state complexity of basic operations for prefix-free regular languages. The nondeterministic state complexity of an operation is the number of states that are necessary and sufficient in the worst-case for a minimal nondeterministic finite-state automaton that accepts the language obtained from the operation. We establish the precise state complexity of caten...

We deene the nondeterministic complexity of a nite automaton and show that there exist, for any integer p 1, automata which need (k 1=p) nondeterministic transitions to spell words of length k. This leads to a subdivision of the family of recognizable M-subsets of a free monoid into a hierarchy whose members are indexed by polynomials, where M denotes the Min{Plus semiring.

We prove: (1) every language accepted by a two-way nondeterministic pushdown automaton can be recognized on a random access machine in O(n3/log n) time; (2) every language accepted by a loop-free two-way nondeterministic pushdown automaton can be recognized in O(n3/log 2 n) time; (3) every context-free language can be recognized onqine in O(n3/log z n) time. We improve the results of Aho, Hopcr...

We propose a modular design of tabular parsing algorithms for treeadjoining languages. The modularity is made possible by a separation of the parsing strategy from the mechanism of tabulation. The parsing strategy is expressed in terms of the construction of a nondeterministic automaton from a grammar; three distinct types of automaton will be discussed. The mechanism of tabulation leads to the...