Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantified Propositional Logspace Reasoning   In this paper, we develop a quantified propositional proof systems that
corresponds to logarithmic-space reasoning. We begin by defining a class
SigmaCNF(2) of quantified formulas that can be evaluated in log space. Then our
new proof system GL^* is defined as G_1^* with cuts restricted to SigmaCNF(2)
formulas and no cut formula that is not quantifier free contains a free
variable that does not appear in the final formula.
  To show that GL^* is strong enough to capture log space reasoning, we
translate theorems of VL into a family of tautologies that have polynomial-size
GL^* proofs. VL is a theory of bounded arithmetic that is known to correspond
to logarithmic-space reasoning. To do the translation, we find an appropriate
axiomatization of VL, and put VL proofs into a new normal form.
  To show that GL^* is not too strong, we prove the soundness of GL^* in such a
way that it can be formalized in VL. This is done by giving a logarithmic-space
algorithm that witnesses GL^* proofs.

25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-fin