DS-1994-03:
Drost, Nicoline Johanna
(1994)
*Process Theory and Equation Solving.*
Doctoral thesis, University of Amsterdam.

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## Abstract

This thesis belongs to the field of process theories and process algebras.

In the first part the model of Rem and Kaldewaij for

communicating processes is analyzed, which shows that their definitions in fact

describe two different models, the first based on prefix-closed trace

structures, the second on trace structures with complete traces. In this

dissertation, both models are described in terms of signature, domain and

axioms. This reveals some problematic properties of the models. The first does

not enable an adequate definition of sequential composition.

In the second model all previous actions are erased in case of succesful

and unsuccessful communication.

The models are combined into a new model that doesn't have these properties.

A discinction is made between successful and unsuccessful terminations.

A complete axiomatisation for this model is presented. Two operators are added

that generate processes with infinitely long executions of infinite choices.

Axioms for these operators are presented. The example for verification

is the alternating bit protocol.

The second topic in this thesis is equation solving in process algebras.

This is useful for specification and implementation of systems with process

algebras. Full specification with an incomplete implementation then leads to

an equation. Equation solving results in a description of all solutions of

missing parts.

Equation solving in astract algebras also plays a role in logic

programming, where it is referred to as unification. The thesis presents

unification algorithms for a number of small process algebras, inspired

by the algebra ACP (Bergstra and Klop). All algebras contain a non-empty

set of constants for atomic actions, and a special constant for

non-successful termination. The first algebra contains the nondeterministic

choice operator as its only operator. This algebra is isomorphic with the

algebra of sets with union and the empy set. A improved version of an

existing unification algorithm for {\em sets} of equations is presented.

The second algebra contains the operators nondeterministic choice and action

prefix. The domain of the algebra also contains infinite processes, that are

described by means of guarded recursive specifications. This algebra turns out

to be finitary. An algorithm is presented that produces a complete set of

most general unifiers for arbitrary sets of equations.

This algorithm is based on transformation rules. When in equations choices do

not contain free variables, the worst case complexity is exponential in the

size of the input, otherwise it is super exponential.

Thus, the algorithm is only usable in the case of small inputs.

The third and last algorithm contains the operators nondeterministic choice and

sequential composition. The algebra contains no finite processes. This algebra

turns out to be finitary and there is thus no unification algorithm that

terminates for each set of equations. An algorithm is presented that

terminates for sets of equations which contain a closed term on one of the

sides. For this input the worst case complexity is exponential in the length

of the input if choices contain no free variables or terms that start with a

variable. This algorithm is only useful for small inputs.

Item Type: | Thesis (Doctoral) |
---|---|

Report Nr: | DS-1994-03 |

Series Name: | ILLC Dissertation (DS) Series |

Year: | 1994 |

Subjects: | Logic |

Depositing User: | Dr Marco Vervoort |

Date Deposited: | 14 Jun 2022 15:16 |

Last Modified: | 14 Jun 2022 15:16 |

URI: | https://eprints.illc.uva.nl/id/eprint/1966 |

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