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On the theory of the PTIME degrees of the recursive sets

1990
*
Journal of computer and system sciences (Print)
*

There is an interpretation

doi:10.1016/0022-0000(90)90024-f
fatcat:x6rmsefnxreepkfhrvyveejcnq
*of*first-order arithmetic in*the**theory**of**the**PTIME**degrees**of**the**recursive**sets*. ... There is an interpretation*of*second-order arithmetic in*the*first-order*theory**of**the**PTIME**degrees*. These results characterize*the*Turing*degrees**of**the*first order*theories**of*these structures. ... What is*the*Turing*degree**of**the**theory**of**the**PTIME*many-*one**degrees**of**the**recursive**sets*? A, B, C, K,,, K,, L, P,, Q,, P,, Q, and U*of**recursive**sets*. ...##
###
On the theory of the PTIME degrees of the recursive sets

1988
*
[1988] Proceedings. Structure in Complexity Theory Third Annual Conference
*

There is an interpretation

doi:10.1109/sct.1988.5285
dblp:conf/coco/ShinodaS88
fatcat:n5hbeedjmbfnzgnfoxrw7wdq64
*of*first order arithmetic in*the**theory**of**the**PTIME**degrees**of**the**recursive**sets*. ... There is an interpretation*of*second order arithmetic in*the*first order*theory**of**the**PTIME**degrees*. These results characterize*the*Turing*degrees**of**the*first order*theories**of*these structures. ... What is*the*Turing*degree**of**the**theory**of**the**PTIME*many-*one**degrees**of**the**recursive**sets*? 55 Y $=\emptyset$ , then $q(A^{(e)})(x)=i$ . ...##
###
Page 1271 of Mathematical Reviews Vol. , Issue 95c
[page]

1995
*
Mathematical Reviews
*

*recursion*

*on*natural numbers, in

*the*more general framework

*of*primitive

*recursion*

*on*term algebras. ... It is a very important and difficult problem in

*recursion*

*theory*to characterize

*the*embeddability

*of*finite lattices in

*the*

*recursively*enumerable (r.e.)

*degrees*. ...

##
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Page 6027 of Mathematical Reviews Vol. , Issue 2000i
[page]

2000
*
Mathematical Reviews
*

Bisimulation-invariant

*PTIME*, or*the*modal fragment*of**PTIME*, thus proves to be*one**of**the*very rare cases in which a logical characterization is known in a*setting**of*unordered structures. ... They show that*the*BSS model forces exactly*one*jump*of*unsolv- ability for*the*decidable*sets*, in contrast to*the*situation for type 2*recursion*. ...##
###
Automorphisms in the PTIME-Turing degrees of recursive sets

1997
*
Annals of Pure and Applied Logic
*

an automorphism

doi:10.1016/s0168-0072(95)00065-8
fatcat:63si4h43srcwrnqtp56dju5hum
*of**the*ideal*of**PTIME*-*degrees*below A. ... We consider questions related to*the*rigidity*of**the*structure W,*the*PTZME-Turing*degrees**of**recursive**sets**of*strings together with PTME-Turing reducibility, <pr , and related structures; do these structures ... If X and Y are each*recursive*in*the*other, then X and Y have*the*same Turing*degree*.*The**recursive**sets*are those which are, in*theory*, computable. ...##
###
Page 3692 of Mathematical Reviews Vol. , Issue 99f
[page]

1999
*
Mathematical Reviews
*

A Turing

*degree**of*enumerable*sets*is contiguous if all enumerable*sets**of*that*degree*are also*of**the*same weak-truth-table (wtt)*degree*. ...*The*expository paper under review, a part*of*a volume*on*recent advances in algebraic model*theory*, presents a very readable, self-contained proof*of*Khovanskii’s*the*- orem and some*of*its applications ...##
###
Differences between Resource Bounded Degree Structures

2003
*
Notre Dame Journal of Formal Logic
*

We exhibit a structural difference between

doi:10.1305/ndjfl/1082637612
fatcat:cnjcerxjtvabrbctkkdbqnx4ee
*the*truth-table*degrees**of**the**sets*which are truth-table above 0 and*the**PTIME*-Turing*degrees**of*all*sets*. ... Though*the*structures do not have*the*same isomorphism type, demonstrating this fact relies*on*developing their common*theory*. ... If A and B are*recursive*in each other, we say that they have*the*same Turing*degree*.*The*Turing*degree**of*a*set*is a measurement*of**the*information which is contained in*the*diagram*of*that*set*. ...##
###
Page 6154 of Mathematical Reviews Vol. , Issue 90K
[page]

1990
*
Mathematical Reviews
*

second-order arithmetic is interpretable in

*the**theory**of**PTIME**degrees**of*all*sets**of*binary strings. ... In both conception and proof this extends*the*earlier results*of**the*authors that true first-order arithmetic is interpretable in*the**theory**of**PTIME**degrees**of**recursive**sets**of*binary strings and true ...##
###
Page 8387 of Mathematical Reviews Vol. , Issue 2000m
[page]

2000
*
Mathematical Reviews
*

This survey explores

*the*structural properties*of*polynomial-time bounded reducibilities defined*on**the**recursive**sets*and*of**the*corresponding*degrees*. ... Let w be*the**set**of*standard numbers and K be {(x,i): i¢€ w and x € @")}. We prove that*the**degree**of*w is definable in*the*ideal*of**degrees*below*the**degree**of*K. ...##
###
Collapsing degrees

1988
*
Journal of computer and system sciences (Print)
*

An m-

doi:10.1016/0022-0000(88)90007-4
fatcat:o7kwseb6rfcmjhjhzexqzv7gn4
*degree*is a collection*of**sets*equivalent under polynomial-time many-*one*(Karp) reductions; for example,*the*complete*sets*for NP or PSPACE are m-*degrees*. ... Hartmanis showed that all*the*then known NP-complete*sets*are isomorphic, and conjectured that*the*m-*degree**of**the*NP-complete*sets*collapses, in essence claiming that there is only*one*NP-complete*set*... Since*the*properties*of**sets*studied in*recursive*function*theory*are invariant under*recursive*isomorphisms,*the*significance*of*this corollary is that*the**recursive*m-complete r.e.*sets*are essentially ...##
###
Hyper-polynomial hierarchies and the polynomial jump

2001
*
Theoretical Computer Science
*

Assuming that

doi:10.1016/s0304-3975(00)00193-6
fatcat:52bsonjwfbgnld5ruoeou3yp6m
*the*polynomial hierarchy (PH) does not collapse, we show*the*existence*of*ascending sequences*of**ptime*Turing*degrees**of*length ! ...*The*lack*of*uniform least upper bounds for ascending sequences*of**ptime**degrees*causes*the*limit levels*of*our hyper-polynomial hierarchy to be inherently non-canonical. ... In this generalization*of*classical computability*theory*, admissible*recursion**theory*,*the*hyperarithmetic*sets*play*the*role*of**the*computable*sets*and 1 1 corresponds to*the*computably enumerable*sets*...##
###
Page 16 of Mathematical Reviews Vol. , Issue 82a
[page]

1982
*
Mathematical Reviews
*

By information content he means essentially

*degree**of*nonrecursiveness in*one**of**the*usual*degree*notions. Most*of*these characterizations are in terms*of**the*weak jump A‘"*of*an re.*set*A. (AS? ...*The*compression theorem says roughly that for any element g*of*a so-called measured*set**of*functions*one*can compute n and a*recursive*A such that g is essentially inadequate for n, but A is strongly adequate ...##
###
Tackling Polytype Queries in Inconsistent Databases: Theory and Algorithm

2012
*
Journal of Software
*

To expand query types under a

doi:10.4304/jsw.7.8.1861-1866
fatcat:oleyvdabkvb7xfz2e2avof2are
*set**of*integrity constraints for obtaining consistent answers over inconsistent databases, a computational*theory*is proposed based*on*first-order logic. ... For a rewritable initial query, a consistent identification statement is constructed based*on**the*join graph by*recursive*computation; and*the*statement combines with*the*initial query to construct a new ... Since our method is based*on**the*join graph,*the*third algorithm considers*recursive*computation for subnodes. ...##
###
Page 5878 of Mathematical Reviews Vol. , Issue 98I
[page]

1998
*
Mathematical Reviews
*

Closing

*PTime*under bounded primitive*recursion**on*numbers yields PSpace. ... Known characterizations start with*the**PTime*functions*of*Cob- ham, who employed bounded primitive*recursion**on*notation and*the*initial function (among other simpler*ones*) x'’' (concatenate as many copies ...##
###
On the Complexity of the Universality and Inclusion Problems for Unambiguous Context-Free Grammars

2020
*
Electronic Proceedings in Theoretical Computer Science
*

However, we show that computing

doi:10.4204/eptcs.320.2
fatcat:mkv6x5s2mvhqjg423zjuydhkvm
*the*coin-flip measure*of*an unambiguous context-free language, a quantitative generalisation*of*universality, is hard for*the*long-standing open problem SQRTSUM. ...*The*latter problem has long been known to be decidable and we propose a PSPACE algorithm that works by reduction to*the*zeroness problem*of*recurrence equations with convolution. ... I also thank an anonymous reviewer for his helpful comments*on*a preliminary version*of*this draft. ...
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