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25
Deciding security of protocols against offline guessing attacks
 In Proc. 12th ACM Conference on Computer and Communications Security (CCS’05
, 2005
"... We provide an effective procedure for deciding the existence of offline guessing attacks on security protocols, for a bounded number of sessions. The procedure consists of a constraint solving algorithm for determining satisfiability and equivalence of a class of secondorder Eunification problems ..."
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Cited by 48 (4 self)
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We provide an effective procedure for deciding the existence of offline guessing attacks on security protocols, for a bounded number of sessions. The procedure consists of a constraint solving algorithm for determining satisfiability and equivalence of a class of secondorder Eunification problems, where the equational theory E is presented by a convergent subterm rewriting system. To the best of our knowledge, this is the first decidability result to use the generic definition of offline guessing attacks due to Corin et al. based on static equivalence in the applied pi calculus.
Birewrite systems
, 1996
"... In this article we propose an extension of term rewriting techniques to automate the deduction in monotone preorder theories. To prove an inclusion a ⊆ b from a given set I of them, we generate from I, using a completion procedure, a birewrite system 〈R⊆, R⊇〉, that is, a pair of rewrite relations ..."
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Cited by 29 (9 self)
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In this article we propose an extension of term rewriting techniques to automate the deduction in monotone preorder theories. To prove an inclusion a ⊆ b from a given set I of them, we generate from I, using a completion procedure, a birewrite system 〈R⊆, R⊇〉, that is, a pair of rewrite relations −−− → R ⊆ and −−− → R ⊇ , and seek a common term c such that a −−−→ R ⊆ c and b −−−→
Solvability of context equations with two context variables is decidable
 THE JOURNAL OF SYMBOLIC COMPUTATION
, 1999
"... Context unification is a natural variant of second order unification that represents a generalization of word unification at the same time. While second order unification is wellknown to be undecidable and word unification is decidable it is currently open if solvability of context equations is deci ..."
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Cited by 25 (2 self)
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Context unification is a natural variant of second order unification that represents a generalization of word unification at the same time. While second order unification is wellknown to be undecidable and word unification is decidable it is currently open if solvability of context equations is decidable. We show that solvability of systems of context equations with two context variables is decidable. The context variables may have an arbitrary number of occurrences, and the equations may contain an arbitrary number of individual variables as well. The result holds under the assumption that the first order background signature is finite.
Decidable and undecidable secondorder unification problems
 In Proceedings of the 9th Int. Conf. on Rewriting Techniques and Applications (RTA’98), volume 1379 of LNCS
, 1998
"... Abstract. There is a close relationship between word unification and secondorder unification. This similarity has been exploited for instance for proving decidability of monadic secondorder unification. Word unification can be easily decided by transformation rules (similar to the ones applied in ..."
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Cited by 15 (9 self)
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Abstract. There is a close relationship between word unification and secondorder unification. This similarity has been exploited for instance for proving decidability of monadic secondorder unification. Word unification can be easily decided by transformation rules (similar to the ones applied in higherorder unification procedures) when variables are restricted to occur at most twice. Hence a wellknown open question was the decidability of secondorder unification under this same restriction. Here we answer this question negatively by reducing simultaneous rigid Eunification to secondorder unification. This reduction, together with an inverse reduction found by Degtyarev and Voronkov, states an equivalence relationship between both unification problems. Our reduction is in some sense reversible, providing decidability results for cases when simultaneous rigid Eunification is decidable. This happens, for example, for onevariable problems where the variable occurs at most twice (because rigid Eunification is decidable for just one equation). We also prove decidability when no variable occurs more than once, hence significantly narrowing the gap between decidable and undecidable secondorder unification problems with variable occurrence restrictions. 1
Wellnested context unification
 In CADE 2005, LNCS 3632
"... Abstract. Context unification (CU) is the open problem of solving context equations for trees. We distinguish a new decidable variant of CU– wellnested CU – and present a new unification algorithm that solves wellnested context equations in nondeterministic polynomial time. We show that minimal w ..."
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Cited by 14 (8 self)
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Abstract. Context unification (CU) is the open problem of solving context equations for trees. We distinguish a new decidable variant of CU– wellnested CU – and present a new unification algorithm that solves wellnested context equations in nondeterministic polynomial time. We show that minimal wellnested solutions of context equations can be composed from the material present in the equation (see Theorem 1). This property is wishful when modeling natural language ellipsis in CU. 1
BetaReduction As Unification
, 1996
"... this report, we use a lean version of the usual system of intersection types, whichwe call . Hence, UP is also an appropriate unification problem to characterize typability of terms in . Quite apart from the new light it sheds on fireduction, such an analysis turns out to have several othe ..."
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Cited by 13 (9 self)
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this report, we use a lean version of the usual system of intersection types, whichwe call . Hence, UP is also an appropriate unification problem to characterize typability of terms in . Quite apart from the new light it sheds on fireduction, such an analysis turns out to have several other benefits
Linear SecondOrder Unification and Context Unification with TreeRegular Constraints
 Proc. of the 11th Int. Conference on Rewriting Techniques and Applications (RTA’2000), volume 1833 of LNCS
, 2000
"... Linear SecondOrder Unification and Context Unification are closely related problems. However, their equivalence was never formally proved. Context unification is a restriction of linear secondorder unification. Here we prove that linear secondorder unification can be reduced to context unificatio ..."
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Cited by 12 (3 self)
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Linear SecondOrder Unification and Context Unification are closely related problems. However, their equivalence was never formally proved. Context unification is a restriction of linear secondorder unification. Here we prove that linear secondorder unification can be reduced to context unification with treeregular constraints. Decidability of context unification is still an open question. We comment on the possibility that linear secondorder unification is decidable, if context unification is, and how to get rid of the treeregular constraints. This is done by reducing rankbound treeregular constraints to wordregular constraints.
Tractable and Intractable SecondOrder Matching Problems
 In Proc. 5th Ann. Int. Computing and Combinatorics Conference (COCOON'99), LNCS 1627
, 1999
"... . The secondorder matching problem is the problem of determining, for a finite set {#t i , s i #  i # I} of pairs of a secondorder term t i and a firstorder closed term s i , called a matching expression, whether or not there exists a substitution # such that t i # = s i for each i # I ..."
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Cited by 10 (2 self)
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. The secondorder matching problem is the problem of determining, for a finite set {#t i , s i #  i # I} of pairs of a secondorder term t i and a firstorder closed term s i , called a matching expression, whether or not there exists a substitution # such that t i # = s i for each i # I . It is wellknown that the secondorder matching problem is NPcomplete. In this paper, we introduce the following restrictions of a matching expression: kary, kfv , predicate, ground , and functionfree. Then, we show that the secondorder matching problem is NPcomplete for a unary predicate, a unary ground, a ternary functionfree predicate, a binary functionfree ground, and an 1fv predicate matching expressions, while it is solvable in polynomial time for a binary functionfree predicate, a unary functionfree, a kfv functionfree (k # 0), and a ground predicate matching expressions. 1 Introduction The unification problem is the problem of determining whether or not any two ter...
Context unification and traversal equations
 In: Proc. of the 12th International Conference on Rewriting Techniques and Applications (RTA’01
, 2001
"... Abstract. Context unification was originally defined by H. Comon in ICALP’92, as the problem of finding a unifier for a set of equations containing firstorder variables and context variables. These context variables have arguments, and can be instantiated by contexts. In other words, they are secon ..."
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Cited by 8 (7 self)
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Abstract. Context unification was originally defined by H. Comon in ICALP’92, as the problem of finding a unifier for a set of equations containing firstorder variables and context variables. These context variables have arguments, and can be instantiated by contexts. In other words, they are secondorder variables that are restricted to be instantiated by linear terms (a linear term is a λexpression λx1 ···λxn.t where every xi occurs exactly once in t). In this paper, we prove that, if the so called rankbound conjecture is true, then the context unification problem is decidable. This is done reducing context unification to solvability of traversal equations (a kind of word unification modulo certain permutations) and then, reducing traversal equations to word equations with regular constraints. 1
Monadic secondorder unification is NPcomplete
 In RTA’04, volume 3091 of LNCS
, 2004
"... Abstract. Bounded SecondOrder Unification is the problem of deciding, for a given secondorder equation t? = u and a positive integer m, whether there exists a unifier σ such that, for every secondorder variable F, the terms instantiated for F have at most m occurrences of every bound variable. I ..."
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Cited by 7 (5 self)
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Abstract. Bounded SecondOrder Unification is the problem of deciding, for a given secondorder equation t? = u and a positive integer m, whether there exists a unifier σ such that, for every secondorder variable F, the terms instantiated for F have at most m occurrences of every bound variable. It is already known that Bounded SecondOrder Unification is decidable and NPhard, whereas general SecondOrder Unification is undecidable. We prove that Bounded SecondOrder Unification is NPcomplete, provided that m is given in unary encoding, by proving that a sizeminimal solution can be represented in polynomial space, and then applying a generalization of Plandowski’s polynomial algorithm that compares compacted terms in polynomial time. 1