The semantic foundations of concurrent constraint programming
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Constant propagation with conditional branches
ACM Transactions on Programming Languages and Systems (TOPLAS)
Static analysis of linear congruence equalities among variables of a program
TAPSOFT '91 Proceedings of the international joint conference on theory and practice of software development on Colloquium on trees in algebra and programming (CAAP '91): vol 1
Array abstractions using semantic analysis of trapezoid congruences
ICS '92 Proceedings of the 6th international conference on Supercomputing
A unifying view of abstract domain design
ACM Computing Surveys (CSUR)
Automatic discovery of linear restraints among variables of a program
POPL '78 Proceedings of the 5th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Systematic design of program analysis frameworks
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Refining and Compressing Abstract Domains
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Comparing the Galois Connection and Widening/Narrowing Approaches to Abstract Interpretation
PLILP '92 Proceedings of the 4th International Symposium on Programming Language Implementation and Logic Programming
Probabilistic Concurrent Constraint Programming
CONCUR '97 Proceedings of the 8th International Conference on Concurrency Theory
Abstract Interpretation of Probabilistic Semantics
SAS '00 Proceedings of the 7th International Symposium on Static Analysis
An Operational Semantics for Probabilistic Concurrent Constraint Programming
ICCL '98 Proceedings of the 1998 International Conference on Computer Languages
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In this paper we design abstract domains for numerical power analysis. These domains are conceived to discover properties of the following type: "The integer (or rational) variable X at a given program point is the numerical power of c with the exponent having a given property π", where c and π are automatically determined. A family of domains is presented, two of these suppose that the exponent can be any natural or integer value, the others include also the analysis of properties of the exponent set. Relevant lattice-theoretic properties of these domains are proved such as the absence of infinite ascending chains and the structure of their meet-irreducible elements. These domains are applied in the analysis of integer powers of imperative programs and in the analysis of probabilistic concurrent programming, with probabilistic non-deterministic choice.