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.

Fast Cellular Automata with Restricted Inter-Cell Communication: Computational Capacity

Abstract: A d-dimensional cellular automaton with sequential input mode is a d-dimensional grid of interconnected interacting finite automata. The distinguished automaton at the origin, the communication cell, is connected to the outside world and fetches the input sequentially. Often in the literature this model is referred to as iterative array. We investigate d-dimensional iterative arrays and one-dimensional cellular automata operating in real and linear time, whose inter-cell communication is restricted to some constant number of bits independent of the number of states. It is known that even one-dimensional one-bit iterative arrays accept rather complicated languages such as a p |p prim or a 2n |n∈ℕ [16]. We show that there is an infinite strict double dimension-bit hierarchy. The computational capacity of the one-dimensional devices in question is compared with the power of communication-restricted two-way cellular automata. It turns out that the relations are quite different from the relations in the unrestricted case. On passing, we obtain an infinite strict bit hierarchy for real-time two-way cellular automata and, moreover, a very dense time hierarchy for every k-bit cellular automata, i.e., just one more time step leads to a proper superfamily of accepted languages.

From automata to formulas: convex integer polyhedra

Abstract: Automata-based representations have recently been investigated as a tool for representing and manipulating sets of integer vectors. In this paper, we study some structural properties of automata accepting the encodings (most significant digit first) of the natural solutions of systems of linear Diophantine inequations, i.e., convex polyhedra in /spl Nopf//sup n/. Based on those structural properties, we develop an algorithm that takes as input an automaton and generates a quantifier-free formula that represents exactly the set of integer vectors accepted by the automaton. In addition, our algorithm generates the minimal Hilbert basis of the linear system. In experiments made with a prototype implementation, we have been able to synthesize in seconds formulas and Hilbert bases from automata with more than 10,000 states.

Execution information rate for some classes of automata

Abstract: We study the Shannon information rate of accepting runs of various forms of automata. This rate is a complexity indicator for executions of these automata. Accepting runs of finite automata and reversal-bounded nondeterministic counter machines, as well as their restrictions and variations, are investigated and are shown, in many cases, to have computable execution rates. We also study the information rate of behaviors in discrete timed automata. We conduct experiments on C programs showing that estimating the information rates for their executions is feasible in many cases.

Two-way cost automata and cost logics over infinite trees

Abstract: Regular cost functions provide a quantitative extension of regular languages that retains most of their important properties, such as expressive power and decidability, at least over finite and infinite words and over finite trees. Much less is known over infinite trees. We consider cost functions over infinite trees defined by an extension of weak monadic second-order logic with a new fixed-point-like operator. We show this logic to be decidable, improving previously known decidability results for cost logics over infinite trees. The proof relies on an equivalence with a form of automata with counters called quasi-weak cost automata, as well as results about converting two-way alternating cost automata to one-way alternating cost automata.