Symbolic reachability analysis using narrowing and its application to verification of cryptographic protocols

Meseguer, José; Thati, Prasanna

doi:10.1007/s10990-007-9000-6

Cited by 78 publications

(37 citation statements)

References 54 publications

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“…It was first used to solve equational unification problems [56] and then generalized to deal with symbolic reachability problems [57]. More formally, the difference between a rewriting step and a narrowing step is that in both cases we use a rewrite rule l ⇒ r to rewrite t at a position p (we express this subterm as t | p ), but narrowing unifies the left-hand side l and t | p ; that is, it uses a substitution σ such that lσ = A t | p σ before actually performing the rewriting step, while in rewriting t | p must be an instance of l (i.e., only matching is required).…”

Section: Searching For Causesmentioning

confidence: 99%

Epidermal Growth Factor Signaling towards Proliferation: Modeling and Logic Inference Using Forward and Backward Search

Riesco

Santos-Buitrago

Rivas

et al. 2017

BioMed Research International

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In biological systems, pathways define complex interaction networks where multiple molecular elements are involved in a series of controlled reactions producing responses to specific biomolecular signals. These biosystems are dynamic and there is a need for mathematical and computational methods able to analyze the symbolic elements and the interactions between them and produce adequate readouts of such systems. In this work, we use rewriting logic to analyze the cellular signaling of epidermal growth factor (EGF) and its cell surface receptor (EGFR) in order to induce cellular proliferation. Signaling is initiated by binding the ligand protein EGF to the membrane-bound receptor EGFR so as to trigger a reactions path which have several linked elements through the cell from the membrane till the nucleus. We present two different types of search for analyzing the EGF/proliferation system with the help of Pathway Logic tool, which provides a knowledge-based development environment to carry out the modeling of the signaling. The first one is a standard (forward) search. The second one is a novel approach based on narrowing, which allows us to trace backwards the causes of a given final state. The analysis allows the identification of critical elements that have to be activated to provoke proliferation.

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Section: Searching For Causesmentioning

confidence: 99%

Epidermal Growth Factor Signaling towards Proliferation: Modeling and Logic Inference Using Forward and Backward Search

Riesco

Santos-Buitrago

Rivas

et al. 2017

BioMed Research International

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“…This ensures that all rewrites with rules in R must take place at the top of the term. In practice, many concurrent systems, including object-oriented systems and communication protocols, can be specified by topmost rewrite theories [16].…”

Section: Preliminariesmentioning

confidence: 99%

“…This paper further develops previous efforts to use rewriting logic and narrowing to perform symbolic model checking of infinite-state systems. 1 Those efforts have gradually increased the expressiveness of the properties that can be verified, first focusing on reachability analysis [16] and then expanding the range to general LTL formulas [1,6]. It is by now clear that state-based temporal logics are not expressive enough to deal with properties involving events, such as message sends and receives; and that the temporal logic of rewriting [14] is a perfect match-at the level of property specification-for rewriting logic-at the level of system specification-so that both can be used seamlessly as a tandem for model checking.…”

Section: Introductionmentioning

confidence: 99%

Infinite-State Model Checking of LTLR Formulas Using Narrowing

Bae

Meseguer

2014

Lecture Notes in Computer Science

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The linear temporal logic of rewriting (LTLR) is a simple extension of LTL that adds spatial action patterns to the logic, expressing that a specific instance of an action described by a rewrite rule has been performed. Although the theory and algorithms of LTLR for finite-state model checking are well-developed [2], no theoretical foundations have yet been developed for infinite-state LTLR model checking. The main goal of this paper is to develop such foundations for narrowing-based logical model checking of LTLR properties. A key theme in this paper is the systematic relationship, in the form of a simulation with remarkably good properties, between the concrete state space and the symbolic state space. A related theme is the use of additional state space reduction methods, such as folding and equational abstractions, that can in some cases yield a finite symbolic state space.1 The temporal logics that can be verified by infinite-state model checking techniques are generally less expressive than those supported by finite-state model checkers.

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“…Narrowing [2] is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications [18,20]. Narrowing can be described as a modification of term rewriting in which matching is replaced by unification so, in a derivation starting from a goal expression, it is able to deduce the instantiation of the variables of the goal expression that is needed for the computation to progress.…”

Section: Introductionmentioning

confidence: 99%

“…under the term rewriting system (TRS) { f (0, 1) → 2, coin → 0, coin → 1} the term rewriting derivation f (X, X)[X/coin] → * 2 cannot be lifted by any narrowing derivation. Several variants and extensions of narrowing have been developed in order to improve that result under certain assumptions or for particular classes of term rewriting systems [19,18,9].…”

Section: Introductionmentioning

confidence: 99%

Lifting Term Rewriting Derivations in Constructor Systems by Using Generators

Riesco

Rodríguez-Hortalá²

2015

Electron. Proc. Theor. Comput. Sci.

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Narrowing is a procedure that was first studied in the context of equational E-unification and that has been used in a wide range of applications. The classic completeness result due to Hullot states that any term rewriting derivation starting from an instance of an expression can be 'lifted' to a narrowing derivation, whenever the substitution employed is normalized. In this paper we adapt the generatorbased extra-variables-elimination transformation used in functional-logic programming to overcome that limitation, so we are able to lift term rewriting derivations starting from arbitrary instances of expressions. The proposed technique is limited to left-linear constructor systems and to derivations reaching a ground expression. We also present a Maude-based implementation of the technique, using natural rewriting for the on-demand evaluation strategy.

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Symbolic reachability analysis using narrowing and its application to verification of cryptographic protocols

Cited by 78 publications

References 54 publications

Epidermal Growth Factor Signaling towards Proliferation: Modeling and Logic Inference Using Forward and Backward Search

Epidermal Growth Factor Signaling towards Proliferation: Modeling and Logic Inference Using Forward and Backward Search

Infinite-State Model Checking of LTLR Formulas Using Narrowing

Lifting Term Rewriting Derivations in Constructor Systems by Using Generators

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