The complexity of regular abstractions of one-counter languages

被引：6

作者：

Atig, Mohamed Faouzi ^{[1
]}

Chistikov, Dmitry ^{[2
]}

Hofman, Piotr ^{[3
,4
]}

Kumar, K. Narayan ^{[5
]}

Saivasan, Prakash ^{[5
,6
]}

Zetzsche, Georg ^{[3
,4
]}

机构：

[1] Uppsala Univ, Uppsala, Sweden

[2] Max Planck Inst Software Syst MPI SWS, Kaiserslautern, Germany

[3] Univ Paris Saclay, CNRS, LSV, St Aubin, France

[4] Univ Paris Saclay, ENS Cachan, St Aubin, France

[5] Chennai Math Inst, Madras, Tamil Nadu, India

[6] Univ Kaiserslautern, Kaiserslautern, Germany

来源：

PROCEEDINGS OF THE 31ST ANNUAL ACM-IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS 2016) | 2016年

关键词：

one-counter automata; upward closure; downward closure; Parikh image;

D O I：

10.1145/2933575.2934561

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We study the computational and descriptional complexity of the following transformation: Given a one-counter automaton (OCA) A, construct a nondeterministic finite automaton (NFA) B that recognizes an abstraction of the language L (A) : its (1) downward closure, (2) upward closure, or (3) Parikh image. For the Parikh image over a fixed alphabet and for the upward and downward closures, we find polynomial-time algorithms that compute such an NFA. For the Parikh image with the alphabet as part of the input, we find a quasi-polynomial time algorithm and prove a completeness result: we construct a sequence of OCA that admits a polynomial-time algorithm iff there is one for all OCA. For all three abstractions, it was previously unknown whether appropriate NFA of sub-exponential size exist.

引用

页码：207 / 216

页数：10

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