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48
Rewriting for Cryptographic Protocol Verification
, 1999
"... . On a case study, we present a new approach for verifying cryptographic protocols, based on rewriting and on tree automata techniques. Protocols are operationally described using Term Rewriting Systems and the initial set of communication requests is described by a tree automaton. Starting from ..."
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Cited by 57 (8 self)
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. On a case study, we present a new approach for verifying cryptographic protocols, based on rewriting and on tree automata techniques. Protocols are operationally described using Term Rewriting Systems and the initial set of communication requests is described by a tree automaton. Starting from these two representations, we automatically compute an overapproximation of the set of exchanged messages (also recognized by a tree automaton). Then, proving classical properties like confidentiality or authentication can be done by automatically showing that the intersection between the approximation and a set of prohibited behaviors is the empty set. Furthermore, this method enjoys a simple and powerful way to describe intruder work, the ability to consider an unbounded number of parties, an unbounded number of interleaved sessions, and a theoretical property ensuring safeness of the approximation. Introduction In this paper, we present a new way of verifying cryptographic pro...
Decidable Approximations of Sets of Descendants and Sets of Normal Forms
, 1997
"... We present here decidable approximations of sets of descendants and sets of normal forms of Term Rewriting Systems, based on specific tree automata techniques. In the context of rewriting logic, a Term Rewriting System is a program, and a normal form is a result of the program. Thus, approximations ..."
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Cited by 42 (13 self)
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We present here decidable approximations of sets of descendants and sets of normal forms of Term Rewriting Systems, based on specific tree automata techniques. In the context of rewriting logic, a Term Rewriting System is a program, and a normal form is a result of the program. Thus, approximations of sets of descendants and sets of normal forms provide tools for analysing a few properties of programs: we show how to compute a superset of results, to prove the sufficient completeness property, or to find a criterion for proving termination under a specific strategy, the sequential reduction strategy.
The Regular Viewpoint on PAProcesses
 Theoretical Computer Science
, 1999
"... PA is the process algebra allowing nondeterminism, sequential and parallel compositions, and recursion. We suggest viewing PAprocesses as trees, and using treeautomata techniques for verification problems on PA. Our main result is that the set of iterated predecessors of a regular set of PAproce ..."
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Cited by 40 (1 self)
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PA is the process algebra allowing nondeterminism, sequential and parallel compositions, and recursion. We suggest viewing PAprocesses as trees, and using treeautomata techniques for verification problems on PA. Our main result is that the set of iterated predecessors of a regular set of PAprocesses is a regular tree language, and similarly for iterated successors. Furthermore, the corresponding treeautomata can be built effectively in polynomialtime. This has many immediate applications to verification problems for PAprocesses, among which a simple and general modelchecking algorithm.
Extrapolating Tree Transformations
, 2002
"... We consider the framework of regular tree model checking where sets of configurations of a system are represented by regular tree languages and its dynamics is modeled by a term rewriting system (or a regular tree transducer). We focus on the computation of the reachability set R # (L) where R i ..."
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Cited by 25 (6 self)
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We consider the framework of regular tree model checking where sets of configurations of a system are represented by regular tree languages and its dynamics is modeled by a term rewriting system (or a regular tree transducer). We focus on the computation of the reachability set R # (L) where R is a regular tree transducer and L is a regular tree language. The construction
Open Problems in Rewriting
 Proceeding of the Fifth International Conference on Rewriting Techniques and Application (Montreal, Canada), LNCS 690
, 1991
"... Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27 ..."
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Cited by 19 (2 self)
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Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27, 28, 44, 56,57,76, 82, 81#; one edited collection of papers #1#; four monographs #3, 12,55,65#; and seven books #four of them still in progress# #8,9, 35, 54, 60,75, 84#. To encourage and stimulate continued progress in this area, wehave collected #with the help of colleagues# a number of problems that appear to us to be of interest and regarding whichwe do not know the answer. Questions on rewriting and other equational paradigms have been included; manyhave not aged su#ciently to be accorded the appellation #open problem". Wehave limited ourselves to theoretical questions, though there are certainly many additional interesting questions relating to applications and implementation
The power of extended topdown tree transducers
 SIAM J. COMPUT
, 2008
"... Unfortunately, the class of transformations computed by linear extended topdown tree transducers with regular lookahead is not closed under composition. It is shown that the class of transformations computed by certain linear bimorphisms coincides with the previously mentioned class. Moreover, it ..."
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Cited by 17 (15 self)
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Unfortunately, the class of transformations computed by linear extended topdown tree transducers with regular lookahead is not closed under composition. It is shown that the class of transformations computed by certain linear bimorphisms coincides with the previously mentioned class. Moreover, it is demonstrated that every linear epsilonfree extended topdown tree transducer with regular lookahead can be implemented by a linear multi bottomup tree transducer. The class of transformations computed by the latter device is shown to be closed under composition, and to be included in the composition of the class of transformations computed by topdown tree transducers with itself. More precisely, it constitutes the composition closure of the class of transformations computed by nitecopying topdown tree transducers.
On the Parallel Complexity of Tree Automata
 Proceedings of the 12th International Conference on Rewrite Techniques and Applications (RTA 2001), Utrecht (The Netherlands), number 2051 in Lecture Notes in Computer Science
, 2001
"... We determine the parallel complexity of several (uniform) membership problems for recognizable tree languages. Furthermore we show that the word problem for a xed nitely presented algebra is in . ..."
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Cited by 13 (3 self)
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We determine the parallel complexity of several (uniform) membership problems for recognizable tree languages. Furthermore we show that the word problem for a xed nitely presented algebra is in .
Regular Sets of Descendants for Constructorbased Rewrite Systems
, 1999
"... . Starting from the regular tree language E of ground constructorinstances of any linear term, we build a nite tree automaton that recognizes the set of descendants R (E) of E for a constructorbased term rewrite system whose righthandsides fulll the following three restrictions : linearity, ..."
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Cited by 12 (3 self)
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. Starting from the regular tree language E of ground constructorinstances of any linear term, we build a nite tree automaton that recognizes the set of descendants R (E) of E for a constructorbased term rewrite system whose righthandsides fulll the following three restrictions : linearity, no nested function symbols, function arguments are variables or ground terms. Note that leftlinearity is not assumed. We next present several applications. 1 Introduction Tree automata have already been applied to many areas of computer science, and in particular to rewriting techniques [2]. In comparison with more sophisticated renements, nite tree automata are obviously less powerful, but have plenty of good properties and lead to much simpler algorithms from a practical point of view. Because of potential applications to automated deduction and program validation, the problem of expressing by a nite tree automaton the transitive closure of a regular set E of ground terms with resp...
Recognizing boolean closed Atree languages with membership conditional mechanism
 In 14 th International Conference on Rewriting Techniques and Applications, volume 2706 of Lecture notes in computer science
, 2003
"... Abstract. This paper provides an algorithm to compute the complement of tree languages recognizable with ATA (tree automata with associativity axioms [16]). Due to this closure property together with the previously obtained results, we know that the class is boolean closed, while keeping recognizab ..."
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Cited by 10 (1 self)
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Abstract. This paper provides an algorithm to compute the complement of tree languages recognizable with ATA (tree automata with associativity axioms [16]). Due to this closure property together with the previously obtained results, we know that the class is boolean closed, while keeping recognizability of Aclosures of regular tree languages. In the proof of the main result, a new framework of tree automata, called sequencetree automata, is introduced as a generalization of Lugiez and Dal Zilio’s multitree automata [14] of an associativity case. It is also shown that recognizable Atree languages are closed under a onestep rewrite relation in case of ground Aterm rewriting. This result allows us to compute an underapproximation of Arewrite descendants of recognizable Atree languages with arbitrary accuracy. 1