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27
Rewriting Logic as a Logical and Semantic Framework
, 1993
"... Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are und ..."
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Cited by 147 (52 self)
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Rewriting logic [72] is proposed as a logical framework in which other logics can be represented, and as a semantic framework for the specification of languages and systems. Using concepts from the theory of general logics [70], representations of an object logic L in a framework logic F are understood as mappings L ! F that translate one logic into the other in a conservative way. The ease with which such maps can be defined for a number of quite different logics of interest, including equational logic, Horn logic with equality, linear logic, logics with quantifiers, and any sequent calculus presentation of a logic for a very general notion of "sequent," is discussed in detail. Using the fact that rewriting logic is reflective, it is often possible to reify inside rewriting logic itself a representation map L ! RWLogic for the finitely presentable theories of L. Such a reification takes the form of a map between the abstract data types representing the finitary theories of...
A Compositional Logic for Proving Security Properties of Protocols
 Journal of Computer Security
, 2002
"... We present a logic for proving security properties of protocols that use nonces (randomly generated numbers that uniquely identify a protocol session) and publickey cryptography. The logic, designed around a process calculus with actions for each possible protocol step, consists of axioms about ..."
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Cited by 50 (12 self)
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We present a logic for proving security properties of protocols that use nonces (randomly generated numbers that uniquely identify a protocol session) and publickey cryptography. The logic, designed around a process calculus with actions for each possible protocol step, consists of axioms about protocol actions and inference rules that yield assertions about protocols composed of multiple steps. Although assertions are written using only steps of the protocol, the logic is sound in a stronger sense: each provable assertion about an action or sequence of actions holds in any run of the protocol that contains the given actions and arbitrary additional actions by a malicious attacker. This approach lets us prove security properties of protocols under attack while reasoning only about the sequence of actions taken by honest parties to the protocol. The main securityspecific parts of the proof system are rules for reasoning about the set of messages that could reveal secret data and an invariant rule called the "honesty rule." 1
Algebraic Theories for NamePassing Calculi
, 1996
"... In a theory of processes the names are atomic data items which can be exchanged and tested for identity. A wellknown example of a calculus for namepassing is the πcalculus, where names additionally are used as communication ports. We provide complete axiomatisations of late and early bisimulation ..."
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Cited by 41 (10 self)
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In a theory of processes the names are atomic data items which can be exchanged and tested for identity. A wellknown example of a calculus for namepassing is the πcalculus, where names additionally are used as communication ports. We provide complete axiomatisations of late and early bisimulation equivalences in such calculi. Since neither of the equivalences is a congruence we also axiomatise the corresponding largest congruences. We consider a few variations of the signature of the language; among these, a calculus of deterministic processes which is reminiscent of sequential functional programs with a conditional construct. Most of our axioms are shown to be independent. The axiom systems differ only by a few simple axioms and reveal the similarities and the symmetries of the calculi and the equivalences.
A congruence for Petri Nets
 PNGT’04
, 2004
"... We introduce a way of viewing Petri nets as open systems. This is done by considering a bicategory of cospans over a category of p/t nets and embeddings. We derive a labelled transition system (LTS) semantics for such nets using GIPOs and characterise the resulting congruence. Technically, our resul ..."
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Cited by 23 (10 self)
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We introduce a way of viewing Petri nets as open systems. This is done by considering a bicategory of cospans over a category of p/t nets and embeddings. We derive a labelled transition system (LTS) semantics for such nets using GIPOs and characterise the resulting congruence. Technically, our results are similar to the recent work by Milner on applying the theory of bigraphs to Petri Nets. The two main differences are that we treat p/t nets instead of c/e nets and we deal directly with a category of nets instead of encoding them into bigraphs.
Stably Computable Properties of Network Graphs
 DISTRIBUTED COMPUTING IN SENSOR SYSTEMS: FIRST IEEE INTERNATIONAL CONFERENCE, DCOSS 2005, MARINA DEL REY, CA, USA, JUNE/JULY, 2005, PROCEEDINGS, VOLUME 3560 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2005
"... We consider a scenario in which anonymous, finitestate sensing devices are deployed in an adhoc communication network of arbitrary size and unknown topology, and explore what properties of the network graph can be stably computed by the devices. We show that they can detect whether the network ..."
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Cited by 21 (12 self)
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We consider a scenario in which anonymous, finitestate sensing devices are deployed in an adhoc communication network of arbitrary size and unknown topology, and explore what properties of the network graph can be stably computed by the devices. We show that they can detect whether the network has degree bounded by a constant d, and, if so, organize a computation that achieves asymptotically optimal linear memory use. We define a model of stabilizing inputs to such devices and show that a large class of predicates of the multiset of final input values are stably computable in any weaklyconnected network. We also show
Erratic Fudgets: A Semantic Theory for an Embedded Coordination Language
 SCIENCE OF COMPUTER PROGRAMMING
, 2003
"... The powerful abstraction mechanisms of functional programming languages provide the means to develop domainspecific programming languages within the language itself. Typically, this is realised by designing a set of combinators (higherorder reusable programs) for an application area, and by constr ..."
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Cited by 20 (3 self)
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The powerful abstraction mechanisms of functional programming languages provide the means to develop domainspecific programming languages within the language itself. Typically, this is realised by designing a set of combinators (higherorder reusable programs) for an application area, and by constructing individual applications by combining and coordinating individual combinators. This paper is concerned with a successful example of such an embedded programming language, namely Fudgets, a library of combinators for building graphical user interfaces in the lazy functional language Haskell. The Fudget library has been used to build a number of substantial applications, including a web browser and a proof editor interface to a proof checker for constructive type theory. This paper develops a semantic theory for the nondeterministic stream processors that are at the heart of the Fudget concept. The interaction of two features of stream processors makes the development of such a semantic theory problematic: (i) the sharing of computation provided by the lazy evaluation mechanism of the underlying host language, and (ii) the addition of nondeterministic choice needed to handle the natural concurrency that reactive applications entail We demonstrate that this combination of features in a higherorder functional language can be tamed to provide a tractable semantic theory and induction principles suitable for reasoning about contextual equivalence of Fudgets.
Principles of chemical programming
 In RULE’04, ENTCS. Elsevier
, 2004
"... Abstract The chemical reaction metaphor describes computation in terms of a chemical solution in which molecules interact freely according to reaction rules. Chemical models use the multiset as their basic data structure. Computation proceeds by rewritings of the multiset which consume elements acco ..."
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Cited by 15 (9 self)
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Abstract The chemical reaction metaphor describes computation in terms of a chemical solution in which molecules interact freely according to reaction rules. Chemical models use the multiset as their basic data structure. Computation proceeds by rewritings of the multiset which consume elements according to reaction conditions and produce new elements according to specific transformation rules. Since the introduction of Gamma in the mideighties, many other chemical formalisms have been proposed such as the Cham, the Psystems and various higherorder extensions. The main objective of this paper is to identify a basic calculus containing the very essence of the chemical paradigm and from which extensions can be derived and compared to existing chemical models. 1
HistoryDependent Automata
 ELECTR. NOTES IN TH. COMP. SCI
, 1998
"... In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated in ..."
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Cited by 14 (1 self)
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In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated in the past history of the system. The most interesting example is calculus: channel names can be created by some actions and they can then be referenced by successive actions. Other examples are CCS with localities and the historypreserving semantics of Petri nets. Ordinary automata are an unsatisfactory operational model for these formalisms: infinite automata are obtained for all the systems with in nite computations, even for very simple ones; moreover, the ordinary definition of bisimulation does not apply in these cases, thus preventing the reusage of standard theories and algorithms. In this paper we show that HDautomata are an adequate model for the historydependent formalisms. We pr...
Communicating Evolving Algebras
 Computer Science Logic
, 1993
"... . We develop the first steps of a theory of concurrency within the framework of evolving algebras of Gurevich, with the aim of investigating its suitability for the role of a general framework for modeling concurrent computation. As a basic tool we introduce a `modal' logic of transition rules and r ..."
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Cited by 13 (2 self)
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. We develop the first steps of a theory of concurrency within the framework of evolving algebras of Gurevich, with the aim of investigating its suitability for the role of a general framework for modeling concurrent computation. As a basic tool we introduce a `modal' logic of transition rules and runs, which is, in the context of evolving algebras, just a definitional extension of ordinary first order logic. A notion of independence of rules and runs enables us to introduce a notion of (and notation for) concurrent runs, on which a logical theory of (`true') concurrency may be based. The notion of concurrent run also has (but does not depend on) an interleaving interpretation. Some basic constructs (concurrent composition, addition of guards and updates) and some derived constructs (internal and external choice, sequential composition) on evolving algebras are introduced and investigated. The power of the framework is demonstrated by developing simple and transparent evolving algebra ...