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Non-deterministic Characterisations (1711.03415v1)
Published 9 Nov 2017 in cs.LO and cs.CC
Abstract: In this paper, we extend Jones' result -- that cons-free programming with $k{th}$-order data and a call-by-value strategy characterises EXP$k$TIME -- to a more general setting, including pattern-matching and non-deterministic choice. We show that the addition of non-determinism is unexpectedly powerful in the higher-order setting. Nevertheless, we can obtain a non-deterministic parallel to Jones' hierarchy result by appropriate restricting rule formation.