License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2020.12
URN: urn:nbn:de:0030-drops-116553
URL: https://drops.dagstuhl.de/opus/volltexte/2020/11655/
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Buss, Sam ; Das, Anupam ; Knop, Alexander

Proof Complexity of Systems of (Non-Deterministic) Decision Trees and Branching Programs

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Abstract

This paper studies propositional proof systems in which lines are sequents of decision trees or branching programs, deterministic or non-deterministic. Decision trees (DTs) are represented by a natural term syntax, inducing the system LDT, and non-determinism is modelled by including disjunction, ∨, as primitive (system LNDT). Branching programs generalise DTs to dag-like structures and are duly handled by extension variables in our setting, as is common in proof complexity (systems eLDT and eLNDT). Deterministic and non-deterministic branching programs are natural nonuniform analogues of log-space (L) and nondeterministic log-space (NL), respectively. Thus eLDT and eLNDT serve as natural systems of reasoning corresponding to L and NL, respectively. The main results of the paper are simulation and non-simulation results for tree-like and dag-like proofs in LDT, LNDT, eLDT and eLNDT. We also compare them with Frege systems, constant-depth Frege systems and extended Frege systems.

BibTeX - Entry

@InProceedings{buss_et_al:LIPIcs:2020:11655,
  author =	{Sam Buss and Anupam Das and Alexander Knop},
  title =	{{Proof Complexity of Systems of (Non-Deterministic) Decision Trees and Branching Programs}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Maribel Fern{\'a}ndez and Anca Muscholl},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11655},
  URN =		{urn:nbn:de:0030-drops-116553},
  doi =		{10.4230/LIPIcs.CSL.2020.12},
  annote =	{Keywords: proof complexity, decision trees, branching programs, logspace, sequent calculus, non-determinism, low-depth complexity}
}

Keywords: proof complexity, decision trees, branching programs, logspace, sequent calculus, non-determinism, low-depth complexity
Collection: 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)
Issue Date: 2020
Date of publication: 06.01.2020


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