Petri nets, commutative context-free grammars, and basic parallel processes
Fundamenta Informaticae
Journal of the ACM (JACM)
Normalizable Horn Clauses, Strongly Recognizable Relations, and Spi
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Decidability and Closure Properties of Equational Tree Languages
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
An NP Decision Procedure for Protocol Insecurity with XOR
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
An Efficient Cryptographic Protocol Verifier Based on Prolog Rules
CSFW '01 Proceedings of the 14th IEEE workshop on Computer Security Foundations
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
A survey of algebraic properties used in cryptographic protocols
Journal of Computer Security
Counting and equality constraints for multitree automata
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Two-way equational tree automata for AC-like theories: decidability and closure properties
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Cryptographic protocol analysis on real c code
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Alternation in equational tree automata modulo XOR
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Two-variable logic on data trees and XML reasoning
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Alternating two-way AC-tree automata
Information and Computation
Selecting theories and nonce generation for recursive protocols
Proceedings of the 2007 ACM workshop on Formal methods in security engineering
Reducing protocol analysis with XOR to the XOR-free case in the horn theory based approach
Proceedings of the 15th ACM conference on Computer and communications security
Two-variable logic on data trees and XML reasoning
Journal of the ACM (JACM)
Context-Bounded Analysis for Concurrent Programs with Dynamic Creation of Threads
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Flat and One-Variable Clauses for Single Blind Copying Protocols: The XOR Case
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Forward Analysis of Dynamic Network of Pushdown Systems Is Easier without Order
RP '09 Proceedings of the 3rd International Workshop on Reachability Problems
Deciding security properties for cryptographic protocols. application to key cycles
ACM Transactions on Computational Logic (TOCL)
On the automatic analysis of recursive security protocols with XOR
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Automatic analysis of the security of XOR-based key management schemes
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Expressive languages for path queries over graph-structured data
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Properties of visibly pushdown transducers
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Semi-linear Parikh images of regular expressions via reduction
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Complexity of pattern-based verification for multithreaded programs
Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Efficient reasoning about data trees via integer linear programming
Proceedings of the 14th International Conference on Database Theory
Reducing Protocol Analysis with XOR to the XOR-Free Case in the Horn Theory Based Approach
Journal of Automated Reasoning
Parikh's theorem: A simple and direct automaton construction
Information Processing Letters
Model checking recursive programs with numeric data types
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Deciding key cycles for security protocols
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Presburger modal logic is PSPACE-Complete
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Algorithmic metatheorems for decidable LTL model checking over infinite systems
FOSSACS'10 Proceedings of the 13th international conference on Foundations of Software Science and Computational Structures
Parikh's theorem and descriptional complexity
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
Efficient reasoning about data trees via integer linear programming
ACM Transactions on Database Systems (TODS)
A Perfect Model for Bounded Verification
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
An Automata Model for Trees with Ordered Data Values
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Synchronisation- and reversal-bounded analysis of multithreaded programs with counters
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Weakly-Synchronized ground tree rewriting
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Expressive Languages for Path Queries over Graph-Structured Data
ACM Transactions on Database Systems (TODS)
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Analysis of Recursively Parallel Programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Extending two-variable logic on data trees with order on data values and its automata
ACM Transactions on Computational Logic (TOCL)
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Security protocols employing cryptographic primitives with algebraic properties are conveniently modeled using Horn clauses modulo equational theories. We consider clauses corresponding to the class $\mathcal{H}3$ of Nielson, Nielson and Seidl. We show that modulo the theory ACU of an associative-commutative symbol with unit, as well as its variants like the theory XOR and the theory AG of Abelian groups, unsatisfiability is NP-complete. Also membership and intersection-non-emptiness problems for the closely related class of one-way as well as two-way tree automata modulo these equational theories are NP-complete. A key technical tool is a linear time construction of an existential Presburger formula corresponding to the Parikh image of a context-free language. Our algorithms require deterministic polynomial time using an oracle for existential Presburger formulas, suggesting efficient implementations are possible.