# ML typability is dexptime-complete

- First Online:

DOI: 10.1007/3-540-52590-4_50

- Cite this paper as:
- 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

## 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.

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