Related papers: Buchi Determinization Made Tighter
This paper establishes a lower bound on the number of states necessary in the worst case to simulate an $n$-state two-way nondeterministic finite automaton (2NFA) by a one-way unambiguous finite automaton (UFA). It is proved that for every…
We investigate the worst-case state complexity of reversals of deterministic finite automata with output (DFAOs). In these automata, each state is assigned some output value, rather than simply being labelled final or non-final. This…
Despite its success in producing numerous general results on state-based dynamics, the theory of coalgebra has struggled to accommodate the Buechi acceptance condition---a basic notion in the theory of automata for infinite words or trees.…
Complementation of B\"uchi automata has been studied for over five decades since the formalism was introduced in 1960. Known complementation constructions can be classified into Ramsey-based, determinization-based, rank-based, and…
Given a nondeterministic finite-state automaton (NFA), we aim to estimate the size of an equivalent deterministic finite-state automaton (DFA). We demonstrate that computing the state complexity of an NFA within polynomial precision is…
A non-deterministic automaton running on infinite trees is unambiguous if it has at most one accepting run on every tree. The class of languages recognisable by unambiguous tree automata is still not well-understood. In particular,…
We investigate the accepting state complexity of deterministic finite automata for regular languages obtained by applying one of the following operations to languages accepted by permutation automata: union, quotient, complement,…
We investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent one-way and two-way deterministic finite automata, from a descriptional complexity point of view. We prove that for…
Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from $n$ states to $2^n$ states.…
Complementation and determinization are two fundamental notions in automata theory. The close relationship between the two has been well observed in the literature. In the case of nondeterministic finite automata on finite words (NFA),…
Exclusive nondeterministic finite automata (XNFA) are nondeterministic finite automata with a special acceptance condition. An input is accepted if there is exactly one accepting path in its computation tree. If there are none or more than…
The projected language of a general deterministic automaton with $n$ states is recognizable by a deterministic automaton with $2^{n-1} + 2^{n-m} - 1$ states, where $m$ denotes the number of states incident to unobservable non-loop…
The precise complexity of complementing B\"uchi automata is an intriguing and long standing problem. While optimal complementation techniques for finite automata are simple - it suffices to determinize them using a simple subset…
Previously, self-verifying symmetric difference automata were defined and a tight bound of 2^n-1-1 was shown for state complexity in the unary case. We now consider the non-unary case and show that, for every n at least 2, there is a…
Motivated by the Babai conjecture and the Cerny conjecture, we study the reset thresholds of automata with the transition monoid equal to the full monoid of transformations of the state set. For automata with $n$ states in this class, we…
We show that the problem of checking if a given nondeterministic parity automaton simulates another given nondeterministic parity automaton is NP-hard. We then adapt the techniques used for this result to show that the problem of checking…
We present a language $L_n$ which is recognizable by a probabilistic finite automaton (PFA) with probability $1 - \epsilon$ for all $\epsilon > 0$ with $O(log^2n)$ states, with a deterministic finite automaton (DFA) with O(n) states, but a…
We describe a minimization procedure for nondeterministic B\"uchi automata (NBA). For an automaton A another automaton A_min with the minimal number of states is learned with the help of a SAT-solver. This is done by successively computing…
We study the strength of set-theoretic axioms needed to prove Rabin's theorem on the decidability of the MSO theory of the infinite binary tree. We first show that the complementation theorem for tree automata, which forms the technical…
When omega-regular objectives were first proposed in model-free reinforcement learning (RL) for controlling MDPs, deterministic Rabin automata were used in an attempt to provide a direct translation from their transitions to scalar values.…