Complexity of Linear Standard Theories [chapter]

1Christopher Lynch, Barbara Morawska
Logic for Programming, Artificial Intelligence, and Reasoning  
We give an algorithm for deciding E-uni cation problems for linear standard equational theories (linear equations with all shared variables at a depth less than two) and varity 1 goals (linear equations with no shared variables). We show that the algorithm halts in quadratic time for the non-uniform E-uni cation problem, and linear time if the equational theory is varity 1. The algorithm is still polynomial for the uniform problem. The size of the complete set of uni ers is exponential, but
more » ... ership in that set can be determined in polynomial time. For any goal (not just varity 1) we give a NEXPTIME algorithm. ?? This work was supported by NSF grant number CCR-9712388 and ONR grant number N00014-01-1-0435. . 1 When we refer to an equational theory, we mean a nite presentation of the theory.
doi:10.1007/3-540-45653-8_13 dblp:conf/lpar/LynchM01 fatcat:c35aonbymja5palllxr7jgkdly