16,545 research outputs found
The 2CNF Boolean Formula Satisfiability Problem and the Linear Space Hypothesis
We aim at investigating the solvability/insolvability of nondeterministic
logarithmic-space (NL) decision, search, and optimization problems
parameterized by size parameters using simultaneously polynomial time and
sub-linear space on multi-tape deterministic Turing machines. We are
particularly focused on a special NL-complete problem, 2SAT---the 2CNF Boolean
formula satisfiability problem---parameterized by the number of Boolean
variables. It is shown that 2SAT with variables and clauses can be
solved simultaneously polynomial time and space for an absolute constant . This fact inspires us to
propose a new, practical working hypothesis, called the linear space hypothesis
(LSH), which states that 2SAT---a restricted variant of 2SAT in which each
variable of a given 2CNF formula appears at most 3 times in the form of
literals---cannot be solved simultaneously in polynomial time using strictly
"sub-linear" (i.e., for a certain constant
) space on all instances . An immediate consequence of
this working hypothesis is . Moreover, we use our
hypothesis as a plausible basis to lead to the insolvability of various NL
search problems as well as the nonapproximability of NL optimization problems.
For our investigation, since standard logarithmic-space reductions may no
longer preserve polynomial-time sub-linear-space complexity, we need to
introduce a new, practical notion of "short reduction." It turns out that,
parameterized with the number of variables, is
complete for a syntactically restricted version of NL, called Syntactic
NL, under such short reductions. This fact supports the legitimacy
of our working hypothesis.Comment: (A4, 10pt, 25 pages) This current article extends and corrects its
preliminary report in the Proc. of the 42nd International Symposium on
Mathematical Foundations of Computer Science (MFCS 2017), August 21-25, 2017,
Aalborg, Denmark, Leibniz International Proceedings in Informatics (LIPIcs),
Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik 2017, vol. 83, pp.
62:1-62:14, 201
Drinfeld Functor and Finite-Dimensional Representations of Yangian
We extend the results of Drinfeld on Drinfeld functor to the case l>n. We
present the character of finite-dimensional representations of the Yangian
Y(sl_n) in terms of the Kazhdan-Lusztig polynomials as a consequence.Comment: Latex2e, 17pages, corrected typo
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