Abstract
The word-problem for a finite set of equational axioms between ground terms is the question whether for terms s,t the equation s = t is a consequence. We consider this problem under grammar based compression of terms, in particular compression with singleton tree grammars (STGs) and with directed acyclic graphs (DAGs) as a special case. We show that given a DAG-compressed ground and reduced term rewriting system T, the T-normal form of an STG-compressed term s can be computed in polynomial time, and hence the T-word problem can be solved in polynomial time. This implies that the word problem of STG-compressed terms w.r.t. a set of DAG-compressed ground equations can be decided in polynomial time. If the ground term rewriting system (gTRS) T is STG-compressed, we show NP-hardness of T-normal-form computation. For compressed, reduced gTRSs we show a PSPACE upper bound on the complexity of the normal form computation of STG-compressed terms. Also special cases are considered and a prototypical implementation is presented.
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Schmidt-Schauss, M., Sabel, D., Anis, A. (2011). Congruence Closure of Compressed Terms in Polynomial Time. In: Tinelli, C., Sofronie-Stokkermans, V. (eds) Frontiers of Combining Systems. FroCoS 2011. Lecture Notes in Computer Science(), vol 6989. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24364-6_16
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DOI: https://doi.org/10.1007/978-3-642-24364-6_16
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