Prefix Iteration Research Articles

Complete Axiomatization for Divergent-Sensitive Bisimulations in Basic Process Algebra with Prefix Iteration

We study the divergent-sensitive spectrum of weak bisimulation equivalences in the setting of process algebra. To represent the infinite behavior, we consider the prefix iteration extension of a fragment of Milner's CCS. The prefix iteration operator is a variant on the binary version of the Kleene star operator obtained by restricting the first argument to be an atomic action and allows us to capture the notion of recursion in a pure algebraic way. We investigate four typical divergent-sensitive weak bisimulation equivalences, namely divergent, stable, completed and divergent stable weak bisimulation equivalences from an axiomatic perspective. A lattice of distinguishing axioms is developed and thus pure equational axiomatizations for these congruences are obtained. A large part of the current paper is devoted to a considerable complicated proof for completeness. This work, to some extent, sheds light on distinct semantics of divergence.

Bi-slotted tree based anti-collision protocols for fast tag identification in RFID systems

This paper is intended to present bi-slotted tree based RFID tag anti-collision protocols, bi-slotted query tree algorithm (BSQTA) and bi-slotted collision tracking tree algorithm (BSCTTA). Diminishing prefix overhead and iteration overhead is a significant issue to minimize the anti-collision cost. For fast tag identification, BSQTA and BSCTTA use time divided responses depending on whether the collided bit is `0' or `1' at each tag ID. According to the simulation results, BSQTA and BSCTTA require less time consumption for tag identification than the other tree based RFID tag anti-collision protocols

A Cook’s Tour of Equational Axiomatizations for Prefix Iteration

Prefix iteration is a variation on the original binary version of the<br />Kleene star operation P*Q, obtained by restricting the first argument to be an atomic action, and yields simple iterative behaviours that can be equationally characterized by means of finite collections of axioms. In this paper, we present axiomatic characterizations for a significant fragment of the notions of equivalence and preorder in van Glabbeek's linear-time/branching-time spectrum over Milner's basic CCS extended with prefix iteration. More precisely, we consider ready simulation, simulation, readiness, trace and language semantics, and provide complete (in)equational axiomatizations for each of these notions over BCCS with prefix iteration. All of the axiom systems we present are finite, if so is the set of atomic actions under consideration.

Axiomatizing Prefix Iteration with Silent Steps

Prefix iteration is a variation on the original binary version of the Kleene star operation P * Q , obtained by restricting the first argument to be an atomic action. The interaction of prefix iteration with silent steps is studied in the setting of Milner's basic CCS. Complete equational axiomatizations are given for four notions of behavioural congruence over basic CCS with prefix iteration, viz., branching congruence, η -congruence, delay congruence, and weak congruence. The completeness proofs for η -, delay, and weak congruence are obtained by reduction to the completeness theorem for branching congruence. It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature. The preliminaries and the completeness proofs focus on open terms, i.e., terms that may contain process variables. As a by-product, the ω -completeness of the axiomatizations is obtained, as well as their completeness for closed terms.

A COMPLETE AXIOMATIZATION FOR PREFIX ITERATION IN BRANCHING BISIMULATION

This paper studies the interaction of prefix iteration with the silent step in the setting of branching bisimulation. We present a finite equational axiomatization for Basic Process Algebra with deadlock, empty process and the silent step, extended with prefix iteration, and prove that this axiomatization is complete with respect to rooted branching bisimulation equivalence.

Axiomatizing Prefix Iteration with Silent Steps

<p>Prefix iteration is a variation on the original binary version of the Kleene star operation P*Q, obtained by restricting the first argument to be an atomic action. The interaction of prefix iteration with silent steps is studied in the setting of Milner's basic CCS. Complete equational axiomatizations are given for four notions of behavioural congruence over basic CCS with prefix iteration, viz. branching congruence, eta-congruence, delay congruence and weak congruence. The completeness proofs for eta-, delay, and weak congruence are obtained by reduction to the completeness theorem for branching congruence. It is also argued that the use of the completeness result for branching congruence in obtaining the completeness result for weak congruence leads to a considerable simplification with respect to the only direct proof presented in the literature. The preliminaries and the completeness proofs focus on open terms, i.e. terms that may contain process variables. As a by-product, the omega-completeness of the axiomatizations is obtained as well as their completeness for closed terms.</p><p> </p><p>AMS Subject Classification (1991): 68Q10, 68Q40, 68Q55.<br />CR Subject Classification (1991): D.3.1, F.1.2, F.3.2.<br />Keywords and Phrases: Concurrency, process algebra, basic CCS, prefix iteration, branching bisimulation, eta-bisimulation, delay bisimulation, weak bisimulation, equational logic, complete axiomatizations.</p>

A Complete Equational Axiomatization for Prefix Iteration with Silent Steps

Fokkink ((1994) Inf. Process. Lett. 52: 333{337) has recently proposed a complete<br />equational axiomatization of strong bisimulation equivalence for MPA_delta^*(A_tau),<br />i.e., the language obtained by extending Milner's basic CCS with prefix iteration.<br />Prefix iteration is a variation on the original binary version of the Kleene star operation<br />p*q obtained by restricting the first argument to be an atomic action. In this<br />paper, we extend Fokkink's results to a setting with the unobservable action by<br />giving a complete equational axiomatization of Milner's observation congruence over<br />MPA_delta^*(A_tau ). <br />The axiomatization is obtained by extending Fokkink's axiom system<br />with two of Milner's standard tau-laws and the following three equations that describe<br />the interplay between the silent nature of tau and prefix iteration:<br />tau . x = tau*x<br />a*(x+tau.y) = a*(x+tau.y + a.y)<br />tau.(a*x) = a*(tau.a*x) .<br />Using a technique due to Groote, we also show that the resulting axiomatization is<br />omega-complete, i.e., complete for equality of open terms.<br />AMS Subject Classification (1991): 68Q40, 68Q42.<br />CR Subject Classification (1991): D.3.1, F.3.2, F.4.2.<br />Keywords and Phrases: Minimal Process Algebra, prefix iteration, equational<br />logic, omega-completeness, observation congruence.

A complete equational axiomatization for prefix iteration

Prefix iteration a * x is added to Minimal Process Algebra (MPA δ , which is a subalgebra of BPA δ equivalent to Milner's basic CCS. We present a finite equational axiomatization for MPA * δ , and prove that this axiomatization is complete with respect to strong bisimulation equivalence. To obtain this result, we will set up a term rewriting system, based on the axioms, and show that bisimilar terms have the same normal form.