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.

On the Succinctness of Nondeterminism

Abstract: Much is known about the differences in expressiveness and succinctness between nondeterministic and deterministic automata on infinite words. Much less is known about the relative succinctness of the different classes of nondeterministic automata. For example, while the best translation from a nondeterministic Biichi automaton to a nondeterministic co-Biichi automaton is exponential, and involves determinization, no super-linear lower bound is known. This annoying situation, of not being able to use the power of nondeterminism, nor to show that it is powerless, is shared by more problems, with direct applications in formal verification. In this paper we study a family of problems of this class. The problems originate from the study of the expressive power of deterministic Biichi automata: Landweber characterizes languages L ⊆ Σ ω that are recognizable by deterministic Biichi automata as those for which there is a regular language R C Σ * such that L is the limit of R; that is, w ∈ L iff ω has infinitely many prefixes in R. Two other operators that induce a language of infinite words from a language of finite words are co-limit, where w ∈ L iff w has only finitely many prefixes in R, and persistent-limit, where w ∈ L iff almost all the prefixes of ware in R. Both co-limit and persistent-limit define languages that are recognizable by deterministic co-Buchi automata. They define them, however, by means of nondeterministic automata. While co-limit is associated with complementation, persistent-limit is associated with universality. For the three limit operators, the deterministic automata for R and L share the same structure. It is not clear, however, whether and how it is possible to relate nondeterministic automata for R and L, or to relate nondeterministic automata to which different limit operators are applied. In the paper, we show that the situation is involved: in some cases we are able to describe a polynomial translation, whereas in some we present an exponential lower bound. For example, going from a nondeterministic automaton for R to a nondeterministic automaton for its limit is polynomial, whereas going to a nondeterministic automaton for its persistent limit is exponential. Our results show that the contribution of nondeterminism to the succinctness of an automaton does depend upon its semantics.

From Nondeterministic B

Abstract: In this paper we revisit Safra's determinization constructions for automata on infinite words. We show how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions. Determinization is used in numerous applications, such as reasoning about tree automata, satisfiability of CTL*, and realizability and synthesis of logical specifications. The upper bounds for all these applications are reduced by using the smaller deterministic automata produced by our construction. In addition, the parity acceptance conditions allows to use more efficient algorithms (when compared to handling Rabin or Streett acceptance conditions).

Finite Automata In Software Modeling With Semaphores And Deadlock Potential

Abstract: Finite automata with their graphs are an important tool in our Computer Science education. We have been using them for years in our Operating Systems I class, mainly in modeling the process synchronization and Critical Section (CS) problems. Now, we want to extend this method for dead- locks and process scheduling simulations. The intent of this paper is to develop an application of the Finite Automata (FA): DFA (Deterministic Finite Automata) and NFA (Nondeterministic Finite Automata) for software modeling in which the binary semaphores are used and a deadlock may occur. A classic case of two (or more) concurrent processes and two binary semaphores is investigated. Processes with a shared critical section (CS) are considered. We anticipate that this method will be used in the Computer Science education program.

Two-way finite automata with a write-once track

Abstract: The basic finite automata model has been extended over the years with different acceptance modes (nondeterminism, alternation), new or improved devices (two-way heads, pebbles, nested pebbles) and with cooperation. None of these additions permits recognition of non-regular languages. The purpose of this work is to investigate a new kind of automata which is inspired by an extension of 2DPDAs. Mogensen enhanced these with what he called a WORM (write once, read many) track and showed that Cook's linear-time simulation result still holds. Here we trade the pushdown store for nondeterminism or a pebble and show that the languages of these new types of finite automata are still regular. The conjunction of alternation, or of nondeterminism and a pebble permits the recognition of non-regular languages. We give examples of languages that are easy to recognize and of operations that are easy to perform using these WORM tracks under nondeterminism. While somewhat similar to Hennie machines, our models do not require an explicit time bound on their computations.

Automata and Logics for Concurrent Systems: Realizability and Verification

Abstract: Automata are a popular tool to make computer systems accessible to formal methods. While classical finite automata are suitable to model sequential boolean programs, models of concurrent systems involve several interacting processes and extend finite-state machines in various respects. This habilitation thesis surveys several such extensions, including pushdown automata with multiple stacks, communicating automata with fixed, parameterized, or dynamic communication topology, and automata running on words over infinite alphabets. We focus on two major questions of classical automata theory, namely realizability (asking whether a specification has an automata counterpart) and model checking (asking whether a given automaton satisfies its specification).