Finite Presentations of Pregroups and the Identity Problem


We consider finitely generated pregroups, and describe how an appropriately defined rewrite relation over words from a generating alphabet yields a natural partial order for a pregroup structure. We investigate the identity problem for pregroups; that is, the algorithmic determination of whether a word rewrites to the identity element. This problem is undecidable in general, however, we give a dynamic programming algorithm and an algorithm of Oerhle (2004) for free pregroups, and extend them to handle more general pregroup structures suggested in Lambek (1999). Finally, we show that the identity problem for a certain class of non-free pregroups is NP-complete.

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@inproceedings{Jger2005FinitePO, title={Finite Presentations of Pregroups and the Identity Problem}, author={Gerhard J{\"a}ger and Paola Monachesi and Gerald Penn and James Rogers and Shuly Wintner and Alexa H. Mater and James D. Fix}, year={2005} }