arXiv subjects

Sergey Ospichev

Publications and source records attributed to Sergey Ospichev.

2 recordsLinked to original sources

arXiv2020

The Expressiveness of Looping Terms in the Semantic Programming

We consider the language of $Δ_0$-formulas with list terms interpreted over hereditarily finite list superstructures. We study the complexity of reasoning in extensions of the language of $Δ_0$-formulas with non-standard list terms, which represent bounded list search, bounded iteration, and bounded recursion. We prove a number of results on the complexity of model checking and satisfiability for these formulas. In particular, we show that the set of $Δ_0$-formulas with bounded recursive terms true in a given list superstructure $HW(\mathcal{M})$ is non-elementary (it contains the class kEXPTIME, for all $k\geqslant 1$). For $Δ_0$-formulas with restrictions on the usage of iterative and recursive terms, we show lower complexity.

cs.LO↗

arXiv2019

Isomorphism types of Rogers semilattices in the analytical hierarchy

A numbering of a countable family $S$ is a surjective map from the set of natural numbers $ω$ onto $S$. A numbering $ν$ is reducible to a numbering $μ$ if there is an effective procedure which given a $ν$-index of an object from $S$, computes a $μ$-index for the same object. The reducibility between numberings gives rise to a class of upper semilattices, which are usually called Rogers semilattices. The paper studies Rogers semilattices for families $S \subset P(ω)$ belonging to various levels of the analytical hierarchy. We prove that for any non-zero natural numbers $m\neq n$, any non-trivial Rogers semilattice of a $Π^1_m$-computable family cannot be isomorphic to a Rogers semilattice of a $Π^1_n$-computable family. One of the key ingredients of the proof is an application of the result by Downey and Knight on degree spectra of linear orders.

math.LO↗