Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Principles of database and knowledge-base systems, Vol. I
Principles of database and knowledge-base systems, Vol. I
Polymorphic type inference in Prolog by abstract interpretation
Proceedings of the 6th Conference on Logic programming '87
A finite presentation theorem for approximating logic programs
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Handbook of theoretical computer science (vol. B)
Fast and precise regular approximations of logic programs
Proceedings of the eleventh international conference on Logic programming
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Reachability Analysis of Term Rewriting Systems with Timbuk
LPAR '01 Proceedings of the Artificial Intelligence on Logic for Programming
PADL '02 Proceedings of the 4th International Symposium on Practical Aspects of Declarative Languages
Abstracting s-semantincs Using A Model-Theoretic Approach
PLILP '94 Proceedings of the 6th International Symposium on Programming Language Implementation and Logic Programming
A Systematic Construction of Abstract Domains
SAS '94 Proceedings of the First International Static Analysis Symposium on Static Analysis
More Precise Yet Efficient Type Inference for Logic Programs
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Decidable Approximations of Term Rewriting Systems
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Cloning-based context-sensitive pointer alias analysis using binary decision diagrams
Proceedings of the ACM SIGPLAN 2004 conference on Programming language design and implementation
Reachability Analysis over Term Rewriting Systems
Journal of Automated Reasoning
Flow analysis of lazy higher-order functional programs
Theoretical Computer Science
Towards an Efficient Implementation of Tree Automata Completion
AMAST 2008 Proceedings of the 12th international conference on Algebraic Methodology and Software Technology
Rewriting approximations for fast prototyping of static analyzers
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Techniques for scaling up analyses based on pre-interpretations
ICLP'05 Proceedings of the 21st international conference on Logic Programming
Characterizing conclusive approximations by logical formulae
RP'11 Proceedings of the 5th international conference on Reachability problems
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We present a technique for approximating the set of reachable terms of a given term rewriting system starting from a given initial regular set of terms. The technique is based on previous work by other authors with the same goal, and yields a finite tree automaton recognising an over-approximation of the set of reachable terms. Our contributions are, firstly, to use Horn clauses to specify the transitions of a possibly infinite-state tree automaton defining (at least) the reachable terms. Apart from being a clear specification, the Horn clause model is the basis for further automatic approximations using standard logic program analysis techniques, yielding finite-state tree automata. The approximations are applied in two stages: first a regular approximation of the model of the given Horn clauses is constructed, and secondly a more precise relational abstraction is built using the first approximation. The analysis uses efficient representations based on BDDs, leading to more scalable implementations. We report on preliminary experimental results.