Abstract
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.
This research was supported in part by NSF CAREER Grant No. 0546844 and a generous gift from Intel. The information presented here does not necessarily reflect the position or the policy of the Government and no official endorsement should be inferred.
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Wassermann, G., Su, Z. (2006). Validity Checking for Finite Automata over Linear Arithmetic Constraints. In: Arun-Kumar, S., Garg, N. (eds) FSTTCS 2006: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2006. Lecture Notes in Computer Science, vol 4337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11944836_37
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DOI: https://doi.org/10.1007/11944836_37
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