The Omega test: a fast and practical integer programming algorithm for dependence analysis
Proceedings of the 1991 ACM/IEEE conference on Supercomputing
The design and implementation of a certifying compiler
PLDI '98 Proceedings of the ACM SIGPLAN 1998 conference on Programming language design and implementation
Deciding Linear Inequalities by Computing Loop Residues
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Validity Checking for Combinations of Theories with Equality
FMCAD '96 Proceedings of the First International Conference on Formal Methods in Computer-Aided Design
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
An Automata-Theoretic Approach to Presburger Arithmetic Constraints (Extended Abstract)
SAS '95 Proceedings of the Second International Symposium on Static Analysis
STeP: Deductive-Algorithmic Verification of Reactive and Real-Time Systems
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
PVS: A Prototype Verification System
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Static Checking of Dynamically Generated Queries in Database Applications
Proceedings of the 26th International Conference on Software Engineering
Precise analysis of string expressions
SAS'03 Proceedings of the 10th international conference on Static analysis
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Decision procedures underlie many program analysis problems. Traditional program analysis algorithms attempt to prove some property about a single, statically-defined program by generating a single constraint. Accordingly, traditional decision procedures take single constraints as input. Extending these traditional program analysis algorithms to reason about potentially infinite languages of programs (as generated by a given metaprogram) requires a new class of decision procedures that reason about languages of constraints. This paper introduces the parameterized class of validity checking problems that take as input a language generator $\mathcal{A}$. The parameters are: (1) the language formalism for $\mathcal{A}$, (2) the theory under which each string in the language of $\mathcal{A}$ is interpretted, and (3) the quantification (existential/universal) of the constraints in the language to which the validity property applies. We introduce such decision problems by presenting an algorithm that decides whether a given finite state automaton $\mathcal{A}$ generates any valid linear arithmetic constraints.