Term-rewriting systems with rule priorities

Baeten, J.C.M.; Bergstra, Jan A.; Klop, Jan Willem; Weijland, W. P.

doi:10.1016/0304-3975(89)90006-6

Cited by 42 publications

(34 citation statements)

References 13 publications

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“…As termination of the original priority rewriting relation of [2] guarantees a semantics for this relation, one can think that IP -termination guarantees a semantics for the IP -rewriting relation. This has to be investigated.…”

Section: Resultsmentioning

confidence: 99%

“…Abstract applies on f (x, y) because the ordering constraint f (x) > x, y is satisfiable by any noetherian ordering having the subterm property. Then, Narrow applies on f (X, Y ) using Rules (1), (2), and (3), according to Definition 6.…”

Section: Example 2 Let Us Consider the Prsmentioning

confidence: 99%

“…In [1,2], priority rewriting systems (PRSs in short) have been introduced. A PRS is a term rewrite system (TRS in short) with a partial ordering on rules, determining a priority between some of them.…”

Section: Introductionmentioning

confidence: 99%

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Termination of Priority Rewriting

Gnaedig

2009

Language and Automata Theory and Applications

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Abstract. Introducing priorities in rewriting increases the expressive power of rules and helps to limit computations. Priority rewriting is used in rule-based programming as well as in functional programming. Termination of priority rewriting is then important to guarantee that programs give a result. We describe an inductive proof method for termination of priority rewriting, relying on an explicit induction on the termination property and working by generating proof trees, which model the rewriting relation by using abstraction and narrowing.

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Section: Resultsmentioning

confidence: 99%

Section: Example 2 Let Us Consider the Prsmentioning

confidence: 99%

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Termination of Priority Rewriting

Gnaedig

2009

Language and Automata Theory and Applications

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“…A Priority BRS (PBRS) is a BRS with rule priorities in the style of [BBKW89], i.e. by introducing a partial ordering on the rules of the reactive system.…”

Section: Priority Brs and Priority Sbrsmentioning

confidence: 99%

Modelling IEEE 802.11 CSMA/CA RTS/CTS with stochastic bigraphs with sharing

Calder

Sevegnani

2014

Form. Asp. Comput.

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Abstract. Stochastic bigraphical reactive systems (SBRS) is a recent formalism for modelling systems that evolve in time and space. However, the underlying spatial model is based on sets of trees and thus cannot represent spatial locations that are shared among several entities in a simple or intuitive way. We adopt an extension of the formalism, SBRS with sharing, in which the topology is modelled by a directed acyclic graph structure. We give an overview of SBRS with sharing, we extend it with rule priorities, and then use it to develop a model of the 802.11 CSMA/CA RTS/CTS protocol with exponential backoff, for an arbitrary network topology with possibly overlapping signals. The model uses sharing to model overlapping connectedness areas, instantaneous prioritised rules for deterministic computations, and stochastic rules with exponential reaction rates to model constant and uniformly distributed timeouts and constant transmission times. Equivalence classes of model states modulo instantaneous reactions yield states in a CTMC that can be analysed using the model checker PRISM. We illustrate the model on a simple example wireless network with three overlapping signals and we present some example quantitative properties.

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“…The three-valued stable model, introduced by Baeten, Bergstra, Klop, and Weijland [23] in term rewriting and by Przymusinski [179] in logic programming, can be used to give meaning to TSSs with negative premises. A three-valued stable model partitions the collection of transitions into three disjoint sets: the set C of transitions that are true, the set F of transitions that are false, and the set U of transitions for which it is unknown whether or not they are true.…”

Section: B2 the Meaning Of Negative Premisesmentioning

confidence: 99%