Emptiness Is Decidable for Asynchronous Cellular Machines

We resume the investigation of asynchronous cellular automata. Originally, these devices were considered in the context of Mazurkiewicz traces, and later generalized to run on arbitrary pomsets without autoconcurrency by Droste and Gastin [3]. While the universality of the accepted language is known to be undecidable [11], we show here that the emptiness is decidable. Our proof relies on a result due to Finkel and Schnoebelen [7] on well-structured transition systems.

[1]  Philippe Schnoebelen,et al.  Well-structured transition systems everywhere! , 2001, Theor. Comput. Sci..

[2]  Anca Muscholl,et al.  Logical Definability on Infinite Traces , 1996, Theor. Comput. Sci..

[3]  Graham Higman,et al.  Ordering by Divisibility in Abstract Algebras , 1952 .

[4]  Dietrich Kuske,et al.  Asynchronous Cellular Automata and Asynchronous Automata for Pomsets , 1998, CONCUR.

[5]  Paul Gastin,et al.  Asynchronous Cellular Automata for Infinite Traces , 1992, ICALP.

[6]  J. Büchi.  Weak Second‐Order Arithmetic and Finite Automata , 1960 .

[7]  Paul Gastin,et al.  Asynchronous Cellular Automata for Pomsets Without Auto-concurrency , 1996, CONCUR.

[8]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[9]  Volker Diekert,et al.  The Book of Traces , 1995 .

[10]  Peter H. Starke,et al.  Processes in Petri Nets , 1981, J. Inf. Process. Cybern..

[11]  Jay L. Gischer,et al.  The Equational Theory of Pomsets , 1988, Theor. Comput. Sci..

[12]  Paul Gastin,et al.  Asynchronous cellular automata for pomsets , 2000, Theor. Comput. Sci..

[13]  Wieslaw Zielonka,et al.  Notes on Finite Asynchronous Automata , 1987, RAIRO Theor. Informatics Appl..