ω-automaton

About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.

Determinism vs. nondeterminism for two-way automata: representing the meaning of states by logical formulæ

Abstract: The question whether nondeterminism is more powerful than determinism for two-way automata is one of the most famous old open problems on the border between formal language theory and automata theory. An exponential gap between the number of states of two-way nondeterministic finite automata (2NFA) and their deterministic counterparts (2DFA) was proved only for some restricted versions of two-way automata up to now. This problem is also related to the famous DLOG vs. NLOG problem. A superpolynomial gap between 2NFAs and 2DFAs on words of polynomial length in the parameter of a complete language of Sipser and Sakoda for the 2DFA vs. 2NFAs problem would imply that DLOG is a proper subset of NLOG. The goal of this paper is first to survey the attempts to solve the 2DFA vs. 2NFA problem. After that we discus why this problem is so hard in spite of the fact that one has a very clear intuition why nondeterminism has to be more powerful than determinism for this computing model. It seems that the hardness lies in the fact that, when trying to prove lower bounds on the number of states of 2DFAs, we are not able to force the states to have a clear meaning. When designing an automaton, we always assign an unambiguous interpretation to each state. In an attempt to capture the concept of meaning of states we introduce a new restriction on the two-way automata: Each state is assigned a logical formula expressing some properties of the input word, and transitions of the automaton must be designed in such a way that the assigned formula is true whenever the automaton is in the given state. In our approach we use propositional formulae with various interpreted atoms. For two such reasonable logics we prove an exponential gap between 2NFAs and 2DFAs. Moreover, using our concept of assigning meaning to the states of 2DFAs we show that there is no exponential gap between general 2NFAs and 2DFAs on inputs of a polynomial length of the complete language of Sakoda and Sipser.

A Note on Automata

Abstract: In this paper, a brief description of finite automata and the class of problems that can be solved by such devices is presented. The main objective is to introduce the concept of length product, illustrate its application to finite automata, and prove some related results.

Reachability analysis of reversal-bounded automata on series–parallel graphs

Abstract: Extensions to finite-state automata on strings, such as multi-head automata or multi-counter automata, have been successfully used to encode many infinite-state non-regular verification problems. In this paper, we consider a generalization of automata-theoretic infinite-state verification from strings to labelled series–parallel graphs. We define a model of non-deterministic, 2-way, concurrent automata working on series–parallel graphs and communicating through shared registers on the nodes of the graph. We consider the following verification problem: given a family of series–parallel graphs described by a context-free graph transformation system (GTS), and a concurrent automaton over series–parallel graphs, is some graph generated by the GTS accepted by the automaton? The general problem is undecidable already for (one-way) multi-head automata over strings. We show that a bounded version, where the automata make a fixed number of reversals along the graph and use a fixed number of shared registers is decidable, even though there is no bound on the sizes of series–parallel graphs generated by the GTS. Our decidability result is based on establishing that the number of context switches can be bounded and on an encoding of the computation of bounded concurrent automata that allows us to reduce the reachability problem to the emptiness problem for pushdown automata.

Experiments with Synchronizing Automata

Abstract: We have improved an algorithm generating synchronizing automata with a large length of the shortest reset words. This has been done by refining some known results concerning bounds on the reset length. Our improvements make possible to consider a number of conjectures and open questions concerning synchronizing automata, checking them for automata with a small number of states and discussing the results. In particular, we have verified the Cerný conjecture for all binary automata with at most 12 states, and all ternary automata with at most 8 states.

Modularization of Regular Growth Automata

Abstract: Regular growth automata form a class of infinite machines, in which all local computations are performed by finite state automata. We present some results which are relevant to application in practice; apart from runtime, the most important one is modularization, that is, abstraction over subroutines. We use the new techniques to prove some results on substitution.