The paper presents a ÿrst reconstruction of Hoare's theory of CSP in terms of partial automata an... more The paper presents a ÿrst reconstruction of Hoare's theory of CSP in terms of partial automata and related coalgebras. We show that the concepts of processes in Hoare (Communicating Sequential Processes, Prentice-Hall, Englewood Cli s, NJ, 1985) are strongly related to the concepts of states for special, namely, ÿnal partial automata. Moreover, we show how the deterministic and nondeterministic operations in can be interpreted in a compatible way by constructions on the semantical level of automata. Based on this, we are able to interpret ÿnite process expressions as representing ÿnite partial automata with designated initial states. In such a way we provide a new method for solving recursive process equations which is based on the concept of ÿnal automata. The coalgebraic reconstruction of CSP allows us to use coinduction as a new proof principle. To make evident the usefulness of this principle we prove some example laws from Hoare (1985).
... (16) Page 10. 478 It is easy to see that this defines an entailment category Ent~(57) for any... more ... (16) Page 10. 478 It is easy to see that this defines an entailment category Ent~(57) for any 57 in "SIGN and that these categories provide a functor Eat ~ : SIGN --+ CAT. ... Page 11. 479 We call (4~, 7,/3) natural if 7 and /3 are natural transformations. ...
Electronic Notes in Theoretical Computer Science, 1999
The paper presents a first step of a coalgebraic analysis of the concept of communicating sequent... more The paper presents a first step of a coalgebraic analysis of the concept of communicating sequential processes as introduced by Hoare in . We make apparent the strong relationship between CSP and partial automata, i.e., special coalgebras. Thereby it turns out that [3] is only dealt with very special automata, namely, with final automata, i.e., automata where the difference between the concepts of state and of process, respectively, disappears. The coalgebraic approach will allow us to develop a proper model theory for process calculi. As first steps in this direction we outline firstly how operations on processes can be generalized in a compatible way to constructions on automata. Secondly, we present a new method for solving recursive process equations. Finally, we discuss that the nondeterminism in CSP can not be modeled based on nondeterministic transition systems usually considered in the coalgebraic literature .
A b s t r a c t . The aim of this paper is an integration of graph grammars with different kinds ... more A b s t r a c t . The aim of this paper is an integration of graph grammars with different kinds of behavioural constraints, in particular with temporal logic constraints. Since the usual algebraic semantics of graph transformation systems is not able to express constrained behaviour we introduce -in analogy to other approaches -a coalgebraic semantics which associates with each system a category of models (deterministic transition systems). Such category has a final object, which includes all finite and infinite transition sequences. The coalgebraic framework makes it possible to introduce a general notion of 'logic of behavioural constraints'. Instances include, for example, graphical consistency constraints and temporal logic constraints. We show that the considered semantics can be restricted to a final coalgebra semantics for systems with behavioural constraints. This result can be instantiated in order to obtain a final coalgebra semantics for graph grammars with temporal logic constraints.
Proceedings of the 7th International Conference on Category Theory and Computer Science, Sep 4, 1997
The notion of an Institution 5] is here taken as the precise formulation for the notion of a logi... more The notion of an Institution 5] is here taken as the precise formulation for the notion of a logical system. By using elementary tools from the core of category theory, we are able to reveal the underlying mathematical structures lying \behind" the logical formulation of the satisfaction condition, and hence to acquire a both suitable and deeper understanding of the institution concept. This allows us to systematically approach the problem of describing and analyzing relations between logical systems. Theorem 2.10 redesigns the notion of an institution to a purely categorical level, so that the satisfaction condition becomes a functorial (and natural) transformation from speci cations to (subcategories of) models and vice versa. This systematic procedure is also applied to discuss and give a natural description for the notions of institution morphism and institution map. The last technical discussion is a careful and detailed analysis of two examples, which tries to outline how the new categorical insights could help in guiding the development of a unifying theory for relations between logical systems.
The theory of algebraic specifications -one of the most important mathematical approaches to the ... more The theory of algebraic specifications -one of the most important mathematical approaches to the specification of abstract data types and software systems -is reviewed from a mathematical and a computer science point of view. The important role of category theory in this area is discussed and it is shown how the following selected problems are treated using category theory: First, a unified framework for specification logics, second compositional semantics, third partial algebras and their specification, and fourth specifications and models for concurrent systems. For the solution of two of the problems classifying categories are used. They allow to present categories of algebras as functor categories and to derive a number of important properties from well known results for functor categories.
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Papers by Uwe Wolter