Fairness in term rewriting systems
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Fairness
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On-the-Fly Model Checking Under Fairness that Exploits Symmetry
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A discipline of multiprogramming: programming theory for distributed applications
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RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Higher-Order and Symbolic Computation
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State/event-based LTL model checking under parametric generalized fairness
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Termination of fair computations in term rewriting
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Model checking LTLR formulas under localized fairness
WRLA'12 Proceedings of the 9th international conference on Rewriting Logic and Its Applications
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Fairness is a rich phenomenon: we have weak and strong fairness, and many different variants of those concepts: transition fairness, object/process fairness, actor fairness, position fairness, and so on, associated with specific models or languages, but lacking a common theoretical framework. This work uses rewriting semantics as a common theoretical framework for fairness. A common thread tying together the different fairness variants is the notion of localization: fairness must often be localized to specific entities in a system. For systems specified as rewrite theories localization can be formalized by making explicit the subset of variables in a rule corresponding to the items that must be localized. In this way, localized fairness becomes a parametric notion, that can be easily specialized to model a very wide range of fairness phenomena. After formalizing these concepts and proving basic results, the paper studies in detail both a relative and an absolute LTL semantics for rewrite theories with localized fairness requirements, and shows that it is always possible to pass from the relative to the absolute semantics by means of a theory transformation. This allows using a standard LTL model checker to check properties under fairness assumptions.