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 States Observability in Deterministic Finite Automata

Abstract: The notion of state observability in systems theory is considered for finite automata and the class of languages recognized by automata with only observable states is investigated. Then one introduces the notion of semi-observable states: their number defines an infinite hierarchy of anti-AFL's in the family of regular languages. The succinctness of considering incompletely specified finite automata is also examined.

Decompositions and complexity of linear automata

Abstract: The Krohn-Rhodes complexity theory for pure (without linearity) automata is well-known. This theory uses an operation of wreath product as a decomposition tool. The main goal of the paper is to introduce the notion of complexity of linear automata. This notion is ultimately related with decompositions of linear automata. The study of these decompositions is the second objective of the paper. In order to define complexity for linear automata, we have to use three operations, namely, triangular product of linear automata, wreath product of pure automata and wreath product of a linear automaton with a pure one which returns a linear automaton. We define the complexity of a linear automaton as the minimal number of operations in the decompositions of the automaton into indecomposable components (atoms). This theory relies on the following parallelism between wreath and triangular products: both of them are terminal objects in the categories of cascade connections of automata. The wreath product is the terminal object in the Krohn-Rhodes theory for pure automata, while the triangular product provides the terminal object for the cascade connections of linear automata.

History-deterministic Parikh Automata

Abstract: Parikh automata extend finite automata by counters that can be tested for membership in a semilinear set, but only at the end of a run. Thereby, they preserve many of the desirable properties of finite automata. Deterministic Parikh automata are strictly weaker than nondeterministic ones, but enjoy better closure and algorithmic properties. This state of affairs motivates the study of intermediate forms of nondeterminism. Here, we investigate history-deterministic Parikh automata, i.e., automata whose nondeterminism can be resolved on the fly. This restricted form of nondeterminism is well-suited for applications which classically call for determinism, e.g., solving games and composition. We show that history-deterministic Parikh automata are strictly more expressive than deterministic ones, incomparable to unambiguous ones, and enjoy almost all of the closure and some of the algorithmic properties of deterministic automata.

Relationships between network parameters and the performance of distributed adaptive-routing algorithms using learning automata in packet-switched datagram networks

Abstract: Large computer networks with dynamic links present special problems in adaptive routing. If the rate of change in the network links is fairly rapid and the changes are nonperiodic, then obtaining the optimal solution for adaptive routing becomes complex and expensive. In addition to the academic value of the solution, the growth of computer networks gives the problem practical importance. Learning automata is logical approach to the above problem. With the right parameter values, learning automata can converge arbitrarily close to the solution for a given network topology and set of conditions. The adaptability of automata reduces the depth of analysis needed for network behavior; the survivability and robustness of the network is also enhanced. Finally, each automaton behaves independently, making automata ideal for distributed decision-making, and minimizing the need for inter-node communication. Previous work on automata and network routing do not address how changes in network parameter values affect the performance of automata-based adaptive routing. Such knowledge is essential if we are to determine the suitability of an automata-based routing algorithm for a given network. Our paper focuses on this question and shows that in packet- switched datagram networks, relationships do indeed exist between network parameters and the performance of distributed adaptive routing algorithms. Additionally, our paper compares the performance and behavior of several types of learning automata, as well as changes in automata behavior over a range of reward and penalty values. Finally, the performance of two automata-based adaptive routing algorithms is compared. Our automaton model is a stochastic, linear, S-model automaton. In other words, the automaton's matrix of action probabilities changes as a result of performance feedback which it receives from the environment, the response to environment feedback is linear, and finally, the feedback it receives from the environment is over a continuous interval.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A Note On the Hierarchy of One-way Data-Independent Multi-Head Finite Automata.

Abstract: In this paper we deal with one-way multi-head data-independent finite automata. A k-head finite automaton A is data-independent, if the position of every head i after step t in the computation on an input w is a function that depends only on the length of the input w, on i and on t (i.e. the trajectories of heads must be the same on the inputs of the same length). It is known that k(k + 1)/2 + 4 heads are better than k for one-way k-head data-independent finite automata. We improve here this result by showing that 2k + 2 heads are better than √ 2k heads for such automata.