Subcubic certificates for CFL reachability

نویسندگان

چکیده

Many problems in interprocedural program analysis can be modeled as the context-free language (CFL) reachability problem on graphs and solved cubic time. Despite years of efforts, there are no known truly sub-cubic algorithms for this problem. We study related certification task: given an instance CFL reachability, small efficiently checkable certificates existence non-existence a path? show that, both scenarios, exist succinct ( O n 2 ) size problem) these checked subcubic (matrix multiplication) The based grammar-based compression paths (for reachability) invariants represented matrix inequalities non-reachability). Thus, lies nondeterministic co-nondeterministic A natural question is whether faster will lead to combinatorial such Boolean satisfiability (SAT). As consequence our results, we that cannot fine-grained reduction from SAT conditional lower bound stronger than ω , unless strong exponential time hypothesis (NSETH) fails. In nutshell, reductions unlikely explain bottleneck reachability. Our results extend equivalent problems: pushdown 2NPDA recognition; well all-pairs For example, describe non-reachability (inductive invariants) observe they multiplication also extract new hardest language, capturing “hard core” all problems.

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ژورنال

عنوان ژورنال: Proceedings of the ACM on programming languages

سال: 2022

ISSN: ['2475-1421']

DOI: https://doi.org/10.1145/3498702