# zbMATH — the first resource for mathematics

Relaxed models for rewriting logic. (English) Zbl 1018.68036
Summary: We modify the definition of the models for rewrite theories by replacing the equality of functors, defined by $$E$$-equal terms, with the equality via a natural isomorphism, called natural symmetry. The relaxation process can be adapted by relaxing all or only a part of the equations, and by relaxing the state structure (and implicitly the computation structure) or just the computation structure. We also consider the subclasses of $$C$$-coherent models, where $$C$$ is a set of equations specifying a collection of commutative symmetry diagrams. The result is a wide palette of model classes which offers more flexibility in modeling concurrent systems.

##### MSC:
 68Q42 Grammars and rewriting systems
CafeOBJ
Full Text:
##### References:
 [1] Diaconescu, R.; Futatsugi, K., cafeobj report: the language, proof techniques, and methodologies for object-oriented algebraic specification, vol. 6 of AMAST series in computing, (1998), World Scientific Singapore [2] D. Lucanu, On the axiomatization of the category of symmetries, Technical report TR-98-03, University “Al.I.Cuza” of Iaşi, Faculty of Computer Science, December 1998. http://www.infoiasi.ro$$/∼$$dlucanu/reports.html. [3] Lucanu, D., Axiomatization of the coherence property for categories of symmetries, (), 386-405 · Zbl 0940.18003 [4] MacLane, S., Category theory for working Mathematician, (1971), Springer Berlin [5] Meseguer, J., Conditional rewriting logic as unified model of concurrency, Theoret. comput. sci., 96, 73-155, (1992) · Zbl 0758.68043 [6] Meseguer, J., A logical theory of concurrent objects and its realization in the maude language, (), 314-390 [7] Meseguer, J.; Montanari, U., Petri nets are monoids, Inform. comput., 88, 2, 105-155, (1990) · Zbl 0711.68077 [8] Piessens, F.; Steegmans, E., Proving semantical equivalence of data specifications, J. pure appl. algebra, 116, 291-322, (1997) · Zbl 0867.68080 [9] Power, A.J., Why tricategories?, Inform. comput., 120, 2, 251-262, (1995) · Zbl 0829.18003 [10] Reichel, H., Initial computability, algebraic specifications and partial algebras, (1987), Clarendon Press Oxford · Zbl 0634.68001 [11] Sassone, V., On the category of Petri net computation, (), 334-348 [12] Sassone, V., An axiomatization of the algebra of Petri net concatenable processes, Theoret. comput. sci., 170, 1-2, 277-296, (1996) · Zbl 0874.68224
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.