A New SAT Encoding of Earley Parsing

Abstract: While the Boolean satisfiability problem (SAT) lies in NP, prodigious work in SAT solvers has allowed for its use in modeling a multitude of practical problems. Stating a problem in SAT can be cumbersome though and so the demand for SAT encodings arises, providing a means to formulate problems or parts of problems in a more intuitive environment. Several algorithms have been proposed in the past to encode context-free grammars as SAT formulae, allowing for the comprehensive construction of many interesting constraints such as at-most k constraints or such ones pertaining to language syntax. In 2011 a new algorithm was proposed, differing from previous ones in it being based on Earley parsing instead of CYK parsing. Although it performed well for interesting groups of grammars it was later found to behave incorrectly for certain inputs. This thesis discusses the flaws in said algorithm, presents a revision of it and argues for the altered algorithm's correctness. The alterations come with a price, however, and both the running time and output size complexities suffer more-than-quadratic blowup. Since no empirical tests have been performed as of yet, it is still unclear what impact this blowup will have on practical instances.