A Measure of Space for Computing over the Reals
Paulin Jacob\'e De Naurois (LIPN)

TL;DR
This paper introduces a new space complexity measure for real computation, defining classes LOGSPACE_W and PSPACE_W, and demonstrates their relationships with known complexity classes and problems.
Contribution
It defines and analyzes new real-space complexity classes LOGSPACE_W and PSPACE_W, establishing their inclusions in existing classes and their relevance for natural algorithms.
Findings
LOGSPACE_W is included in NC^2_R and P_W
Real Circuit Decision Problem is P_R-complete under LOGSPACE_W reductions
PSPACE_W is included in PAR_R
Abstract
We propose a new complexity measure of space for the BSS model of computation. We define LOGSPACE\_W and PSPACE\_W complexity classes over the reals. We prove that LOGSPACE\_W is included in NC^2\_R and in P\_W, i.e. is small enough for being relevant. We prove that the Real Circuit Decision Problem is P\_R-complete under LOGSPACE\_W reductions, i.e. that LOGSPACE\_W is large enough for containing natural algorithms. We also prove that PSPACE\_W is included in PAR\_R.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputability, Logic, AI Algorithms · Complexity and Algorithms in Graphs · Cellular Automata and Applications
