The trace automaton appears to be a useful tool in generating partially-ordered test cases for asynchronous systems. We give an EXPSPACE algorithm which constructs the trace automaton from a given set of asynchronous communicating processes. Conclusions: We introduce the notion of trace automaton of a system of asyn-chronously communicating input-output state machines such that the trace automa...

We prove that the mapping class group of a compact surface with a nite number of punctures and non-empty boundary is order automatic. More precisely, the group is right-orderable, has an automatic structure as described by Mosher, and there exists a nite state automaton that decides, given the Mosher normal forms of two elements of the group, which of them represents the larger element of the g...

This article studies the learnability of classes of pattern languages over automatic groups. It is shown that the class of bounded unions of pattern languages over any finitely generated Abelian automatic group is explanatorily learnable. Furthermore, patterns are considered in which variables occur at most n times. The classes of the languages generated by such patterns as well as the bounded ...

Nekrashevych algebras of self-similar group actions are natural generalizations the classical Leavitt algebras. They discrete analogues corresponding $$C^*$$ -algebras. In particular, Nekrashevych, Clark, Exel, Pardo, Sims and Starling have studied question simplicity algebras, in part, because non-simplicity complex algebra implies -algebra. this paper we give necessary sufficient conditions f...

We say that a finite asynchronous cellular automaton (or more generally, any sequential dynamical system) is π-independent if its set of periodic points are independent of the order that the local functions are applied. In this case, the local functions permute the periodic points, and these permutations generate the dynamics group. We have previously shown that exactly 104 of the possible 22 3...

A model of information confrontation based on a two-dimensional percolation-cellular automaton closed oriented surface is constructed and implemented programmatically. Numerical experiments were performed. theorem the finiteness completely positive topological entropy given cellular formulated proved. As an applied application automaton, retrospective forecast results Russian Presidential elect...

In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a computing unit, a sequential automaton is employed to describe some state transitions, a hierarchical automaton is employed to express the different granula...

We study the dynamic and complexity of generalized Q2R automaton. show existence non-polynomial cycles as well its capability to simulate with synchronous update classical version automaton updated under a block sequential scheme. Furthermore, we that decision problem consisting in determine if given node network changes state is P-Hard.

The critical behavior of charge-density waves (CDWs) in the pinned phase is studied for applied fields increasing toward the threshold field, using recently developed renormalization group techniques and simulations of automaton models. Despite the existence of many metastable states in the pinned state of the CDW, the renormalization group treatment can be used successfully to find the diverge...

The Nottingham group at 2 is the of (formal) power series t+a2t2+a3t3+⋯ in variable t with coefficients ai from field two elements, where operation given by composition series. depth such a largest d⩾1 for which a2=…=ad=0. Only handful finite order (forcedly 2) are explicitly known through formula their coefficients. We argue this paper that it advantageous to describe closed computational form...