Process algebra with backtracking

Abstract

Abstract. An extension of process algebra for modelling processes with backtracking is introduced. This extension is semantically based on processes that transform data because, in our view, backtracking is the undoing of the effects caused by a process in some initial data-state if this process fails. The data-states are given by a data environment, which is a structure that also defines in which data-states guards hold, and how (atomic) actions either transform these states or block and prevent subsequent processes from being executed. State operators are used to relate process terms to a given data environment. Backtracking is axiomatised in a few phases. First guarded commands (conditionals) and a standard ~ype of guards, expressing the enabledness of actions, are added to basic process algebra (process algebra without operators for parallelism) by involving a Boolean algebra. Then the set of actions is partitioned in order to distinguish between different types of behaviour of actions in the scope of a (binary) operator for backtracking. Also functions on actions are defined that change the 'type' of an action. Next an axiom system for modelling processes with backtracking is presented, and it is proved that backtracking is associative, provided that some semantic constraints are satisfied. Finally a method for recursively specifying processes is defined and an example of a recursively defined process with backtracking is provided. An operational semantics is defined relative to the Boolean algebra, describing transitions between process terms labelled with 'guarded actions'. The operational semantics is studied modulo strong bisimulation equivalence.

Strong Splitting Bisimulation Equivalence

“…Splitting bisimilarity is based on a variant of bisimilarity that was defined for the first time in [2]. The formulation given here is closer to the one given in [9]. State operators were added to ACP for the first time in [1].…”

“…Several extensions of ACP [6,5] include conditional expressions of the form ζ :→ p or p ζ q (see e.g. [4,2,9,3]). What is considered to be conditions differs from one extension to another.…”

ToolBus: The Next Generation

“…It is helpful that a backtrack operator similar to the one described in [24] has also been described for Process Algebra [3]. What remains to be studied is how the recovery of tools has to be organized.…”

Structural Operational Semantics

“…However, in the literature we see more and more that SOS definitions are decorated with predicates and/or negative premises. For example, predicates are used to express matters like (un)successful termination, convergence, divergence [10], enabledness [41], maximal delay, and side conditions [165]. Negative premises are used to describe, e.g., deadlock detection [137], sequencing [55], priorities [24,65], probabilistic behaviour [139], urgency [58], and various real [136] and discrete time [23,127,223] settings.…”