Descriptive Complexity of Deterministic Polylogarithmic Time and Space

Autor:	Ferrarotti, Flavio, González, Senén, Torres, José María Turull, Bussche, Jan Van den, Virtema, Jonni
Rok vydání:	2019
Předmět:	Computer Science - Logic in Computer Science
Druh dokumentu:	Working Paper
Popis:	We propose logical characterizations of problems solvable in deterministic polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We introduce a novel two-sorted logic that separates the elements of the input domain from the bit positions needed to address these elements. We prove that the inflationary and partial fixed point vartiants of this logic capture PolylogTime and PolylogSpace, respectively. In the course of proving that our logic indeed captures PolylogTime on finite ordered structures, we introduce a variant of random-access Turing machines that can access the relations and functions of a structure directly. We investigate whether an explicit predicate for the ordering of the domain is needed in our PolylogTime logic. Finally, we present the open problem of finding an exact characterization of order-invariant queries in PolylogTime. Comment: Submitted to the Journal of Computer and System Sciences
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1903.03413 Zobrazit plný text záznamu View this record from Arxiv