The complexity of knowledge representation

Papadimitriou, Christos H.

doi:10.1109/ccc.1996.507686

Cited by 476 publications

(696 citation statements)

References 14 publications

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“…The downside is that, in order to decide one-step deducibility, we now have to solve linear Diophantine equation systems over N. This problem is in general NP-complete [17]. Furthermore, it is quite easy to reduce satisfiability of linear Diophantine equations over N to the intruder deduction problem modulo ACh.…”

Section: Locality In the General Casementioning

confidence: 99%

Intruder Deduction for AC-Like Equational Theories with Homomorphisms

Lafourcade

Lugiez

Treinen

2005

Lecture Notes in Computer Science

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Abstract. Cryptographic protocols are small programs which involve a high level of concurrency and which are difficult to analyze by hand. The most successful methods to verify such protocols rely on rewriting techniques and automated deduction in order to implement or mimic the process calculus describing the protocol execution. We focus on the intruder deduction problem, that is the vulnerability to passive attacks, in presence of several variants of AC -like axioms (from AC to Abelian groups, including the theory of exclusive or ) and homomorphism which are the most frequent axioms arising in cryptographic protocols. Solutions are known for the cases of exclusive or, of Abelian groups, and of homomorphism alone. In this paper we address the combination of these AC -like theories with the law of homomorphism which leads to much more complex decision problems. We prove decidability of the intruder deduction problem in all cases considered. Our decision procedure is in EXPTIME, except for a restricted case in which we have been able to get a PTIME decision procedure using a property of one-counter and pushdown automata.

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Section: Locality In the General Casementioning

confidence: 99%

Intruder Deduction for AC-Like Equational Theories with Homomorphisms

Lafourcade

Lugiez

Treinen

2005

Lecture Notes in Computer Science

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“…The proof of Lemma 5.2 is similar to either the proof of the PSPACE-hardness of the finite automaton intersection problem [28,38] (see also a generalization in [40]) or the proof of the PSPACE-hardness of Reachable Deadlock for a system of communicating processes [44,Theorem 19.10] (see also [29, Appendix AL6]). One can also prove in a similar way that a linearly bounded automaton of size n can be simulated by a 1-safe Petri net of size O(n 2 ) [35].…”

Section: Proof (Sketch)mentioning

confidence: 97%

A Parametric Analysis of the State Explosion Problem in Model Checking

2002

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In model checking, the state-explosion problem occurs when one checks a non-flat system, i.e., a system implicitly described as a synchronized product of elementary subsystems. In this paper, we investigate the complexity of a wide variety of modelchecking problems for non-flat systems under the light of parameterized complexity, taking the number of synchronized components as a parameter. We provide precise complexity measures (in the parameterized sense) for most of the problems we investigate, and evidence that the results are robust.

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“…[21]) used in [7] to show NEXPTIME-hardness of the SUC-CESS problem for nonrecursive logic programming, i.e., the problem of deciding whether a nonrecursive logic program treated as a database query will return a nonempty result.…”

Section: Proofmentioning

confidence: 99%

Query Rewriting with Symmetric Constraints

Koch

2002

Lecture Notes in Computer Science

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We address the problem of answering queries using expressive symmetric inter-schema constraints which allow to establish mappings between several heterogeneous information systems. This problem is of high relevance to data integration, as symmetric constraints are essential for dealing with true concept mismatch and are generalizations of the kinds of mappings supported by both local-as-view and global-as-view approaches that were previously studied in the literature. Moreover, the flexibility gained by using such constraints for data integration is essential for virtual enterprise and e-commerce applications. We first discuss resolution-based methods for computing maximally contained rewritings and characterize computability aspects. Then we propose an alternative but semantically equivalent perspective based on a generalization of results relating to the database-theoretic problem of answering queries using views. This leads to a fast query rewriting algorithm based on AI techniques, which has been implemented and experimentally evaluated.

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The complexity of knowledge representation

Cited by 476 publications

References 14 publications

Intruder Deduction for AC-Like Equational Theories with Homomorphisms

Intruder Deduction for AC-Like Equational Theories with Homomorphisms

A Parametric Analysis of the State Explosion Problem in Model Checking

Query Rewriting with Symmetric Constraints

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