Abstract
We carry out an analysis of typability of terms in ML. Our main result is that this problem is DEXPTIME-hard, where by DEXPTIME we mean DTIME\((2^{n^{O(1)} } )\). This, together with the known exponential-time algorithm that solves the problem, yields the DEXPTIME-completeness result. This settles an open problem of P. Kanellakis and J.C. Mitchell.
Part of our analysis is an algebraic characterization of ML typability in terms of a restricted form of semi-unification, which we identify as acyclic semi-unification. We prove that ML typability and acyclic semi-unification are log-space equivalent problems. We believe this result is of independent interest.
(Extended Summary)
This work is partly supported by NSF grant CCR-8901647 and by a grant of the Polish Ministry of National Education, No. RP.I.09
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Kfoury, A.J., Tiuryn, J., Urzyczyn, P. (1990). ML typability is dexptime-complete. In: Arnold, A. (eds) CAAP '90. CAAP 1990. Lecture Notes in Computer Science, vol 431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52590-4_50
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DOI: https://doi.org/10.1007/3-540-52590-4_50
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