Register-machine based processes

We study extensions of the process algebra axiom system <b>ACP</b> with two recursive operations: the <i>binary Kleene star</i> <sup>*</sup>, which is defined by <i>x</i><sup>*</sup><i>y</i> = <i>x</i>(<i>x</i><sup>*</sup><i>y</i> + <i>y</i>, and the <i>push-down</i> operation <sup>$</sup>, defined by <i>x</i><sup>$</sup><i>y</i> = <i>x</i>((<i>x</i><sup>$</sup><i>y</i>)(<i>x</i><sup>$</sup><i>y</i>)) + <i>y</i>. In this setting it is easy to represent register machine computation, and an equational theory results that is not decidable. In order to increase the expressive power, abstraction is then added: with <i>rooted branching bisimulation equivalence</i> each computable process can be expressed, and with <i>rooted ô-bisimilarity</i> each semi-computable process that initially is finitely branching can be expressed. Moreover, with abstraction and a finite number of auxiliary actions these results can be obtained without binary Kleene star. Finally, we consider two alternatives for the push-down operation. Each of these gives rise to similar results.

[1]  Luca Aceto,et al.  An Equational Axiomatization of Observation Congruence for Prefix Iteration , 1996, AMAST.

[2]  Jan A. Bergstra,et al.  On the Consistency of Koomen's Fair Abstraction Rule , 1987, Theor. Comput. Sci..

[3]  Rob J. van Glabbeek,et al.  Branching time and abstraction in bisimulation semantics , 1996, JACM.

[4]  S C Kleene,et al.  Representation of Events in Nerve Nets and Finite Automata , 1951 .

[5]  Chris Verhoef,et al.  Concrete process algebra , 1995, LICS 1995.

[6]  Luca Aceto,et al.  Axiomatizing Prefix Iteration with Silent Steps , 1995 .

[7]  Jan A. Bergstra,et al.  Decidability of bisimulation equivalence for process generating context-free languages , 1987, JACM.

[8]  Wan Fokkink,et al.  Introduction to Process Algebra , 1999, Texts in Theoretical Computer Science. An EATCS Series.

[9]  Luca Aceto,et al.  A Cook's Tour of Equational Axiomatizations for Prefix Iteration , 1998, FoSSaCS.

[10]  Rob J. van Glabbeek,et al.  A Complete Axiomatization for Branching Bisimulation Congruence of Finite-State Behaviours , 1993, MFCS.

[11]  Jan Friso Groote,et al.  Syntax and semantics of CRL , 1995 .

[12]  Luca Aceto,et al.  An Equational Axiomatization for Multi-Exit Iteration , 1996 .

[13]  Jan A. Bergstra,et al.  Process Algebra with Iteration and Nesting , 1994, Comput. J..

[14]  Jan Friso Groote,et al.  Structured Operational Semantics and Bisimulation as a Congruence , 1992, Inf. Comput..

[15]  Wan Fokkink,et al.  Axiomatizations for the Perpetual Loop in Process Algebra , 1997, ICALP.

[16]  Jan A. Bergstra,et al.  Decidability of Bisimulation Equivalence for Processes Generating Context-Free Languages , 1987, PARLE.

[17]  Luca Aceto,et al.  A menagerie of non-finitely based process semantics over BPA* – from ready simulation to completed traces , 1998, Mathematical Structures in Computer Science.

[18]  Jos C. M. Baeten,et al.  A Congruence Theorem for Structured Operational Semantics with Predicates , 1993, CONCUR.

[19]  Jan A. Bergstra,et al.  Algebra of Communicating Processes with Abstraction , 1985, Theor. Comput. Sci..

[20]  Luca Aceto,et al.  A Coock's Tour of Equational Axiomatizations for Prefix Iteration , 1998 .

[21]  Marvin Minsky,et al.  Computation : finite and infinite machines , 2016 .

[22]  Luca Aceto,et al.  On a Question of A. Salomaa: The Equational Theory of Regular Expressions Over a Singleton Alphabet is not Finitely Based , 1998, Theor. Comput. Sci..

[23]  Luca Aceto,et al.  A Menagerie of Non-Finitely Based Process Semantics over BPA*: From Ready Simulation Semantics to Completed Traces , 1996 .

[24]  Rob J. van Glabbeek.  Axiomatizing Flat Iteration , 1997, CONCUR.

[25]  Rob J. van Glabbeek,et al.  Branching Time and Abstraction in Bisimulation Semantics (Extended Abstract) , 1989, IFIP Congress.

[26]  Jan Friso Groote,et al.  A Complete Equational Axiomatization for MPA with String Iteration , 1995 .

[27]  Wan Fokkink,et al.  A Complete Axiomatization for Prefix Iteration in Branching Bisimulation , 1996, Fundam. Informaticae.

[28]  Jan A. Bergstra,et al.  Process Algebra with Recursive Operations , 2001, Handbook of Process Algebra.

[29]  Jan A. Bergstra,et al.  Non-regular iterators in process algebra , 2001, Theor. Comput. Sci..

[30]  Robin Milner,et al.  A Calculus of Communicating Systems , 1980, Lecture Notes in Computer Science.

[31]  Luca Aceto,et al.  Axiomatizing Prefix Iteration with Silent Steps , 1995, Inf. Comput..

[32]  Viggo Stoltenberg-hansen,et al.  In: Handbook of Logic in Computer Science , 1995 .

[33]  Wan Fokkink,et al.  A Complete Equational Axiomatization for Prefix Iteration , 1994, Inf. Process. Lett..

[34]  Jan A. Bergstra,et al.  Process Algebra for Synchronous Communication , 1984, Inf. Control..

[35]  David Park,et al.  Concurrency and Automata on Infinite Sequences , 1981, Theoretical Computer Science.

[36]  Jan A. Bergstra,et al.  Programs, interfaces and components , 1999 .

[37]  Peter Sewell,et al.  Nonaxiomatisability of Equivalences over Finite State Processes , 1997, Ann. Pure Appl. Log..

[38]  Jan A. Bergstra,et al.  Process algebra with iteration , 1993 .

[39]  Jan A. Bergstra,et al.  Top-Down Design and the Algebra of Communicating Processes , 1985, Sci. Comput. Program..

[40]  Hans Zantema,et al.  Basic Process Algebra with Iteration: Completeness of its Equational Axioms , 1993, Comput. J..