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Temporal verification of reactive systems: safety
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ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
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LOPSTR'02 Proceedings of the 12th international conference on Logic based program synthesis and transformation
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Pentagons: A weakly relational abstract domain for the efficient validation of array accesses
Science of Computer Programming
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VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Efficient strongly relational polyhedral analysis
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
Symbolic methods to enhance the precision of numerical abstract domains
VMCAI'06 Proceedings of the 7th international conference on Verification, Model Checking, and Abstract Interpretation
ESOP'10 Proceedings of the 19th European conference on Programming Languages and Systems
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SAS'07 Proceedings of the 14th international conference on Static Analysis
The Abstract Domain of Parallelotopes
Electronic Notes in Theoretical Computer Science (ENTCS)
Polyhedral analysis using parametric objectives
SAS'12 Proceedings of the 19th international conference on Static Analysis
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Template polyhedra generalize weakly relational domains by specifying arbitrary fixed linear expressions on the left-hand sides of inequalities and undetermined constants on the right. The domain operations required for analysis over template polyhedra can be computed in polynomial time using linear programming. In this paper, we introduce the generalized template polyhedral domain that extends template polyhedra using fixed left-hand side expressions with bilinear forms involving program variables and unknown parameters to the right. We prove that the domain operations over generalized templates can be defined as the "best possible abstractions" of the corresponding polyhedral domain operations. The resulting analysis can straddle the entire space of linear relation analysis starting from the template domain to the full polyhedral domain. We show that analysis in the generalized template domain can be performed by dualizing the join, post-condition and widening operations. We also investigate the special case of template polyhedra wherein each bilinear form has at most two parameters. For this domain, we use the special properties of two dimensional polyhedra and techniques from fractional linear programming to derive domain operations that can be implemented in polynomial time over the number of variables in the program and the size of the polyhedra. We present applications of generalized template polyhedra to strengthen previously obtained invariants by converting them into templates. We describe an experimental evaluation of an implementation over several benchmark systems.