On the structure of logspace probabilistic complexity classes

被引:0
|
作者
Res. and Advanced Development Group, Metamor Software Solutions, 2851 Clover Street, Pittsford, NY 14534, United States [1 ]
机构
来源
SIAM J Comput | / 3卷 / 987-1007期
关键词
Computational complexity - Formal languages - Game theory - Polynomials - Probability - Set theory - Theorem proving;
D O I
暂无
中图分类号
学科分类号
摘要
We investigate hierarchical properties and logspace reductions of languages recognized by logspace probabilistic Turing machines, Arthur-Merlin games, and games against nature with logspace probabilistic verifiers. Each logspace complexity class is decomposed into a hierarchy based on corresponding two-way multihead finite-state automata and we (eventually) prove the separation of the hierarchy levels (even for languages over a single-letter alphabet); furthermore, we show efficient reductions of each logspace complexity class to, or between, low levels of its corresponding hierarchy. We find probabilistic and probabilistic-plus-nondeterministic variants of Savitch's maze threading problem which are logspace complete for PL (the class of languages recognized by logspace probabilistic Turing machines) and, respectively, P (the class of languages recognized by polynomial-time deterministic Turing machines), and which can be recognized by one-way non-sensing two-head (or one-way one-head one-counter) finite-state automata with probabilistic and both probabilistic and nondeterministic states, respectively.
引用
收藏
相关论文
共 50 条
  • [41] Logical characterizations of bounded query classes I. Logspace oracle machines
    Stewart, Iain A.
    Fundamenta Informaticae, 1993, 18 (01) : 65 - 92
  • [42] #NFA Admits an FPRAS: Efficient Enumeration, Counting, and Uniform Generation for Logspace Classes
    Arenas, Marcelo
    Alberto Croquevielle, Luis
    Jayaram, Rajesh
    Riveros, Cristian
    JOURNAL OF THE ACM, 2021, 68 (06)
  • [44] Classifying Problems on Linear Congruences and Abelian Permutation Groups Using Logspace Counting Classes
    V. Arvind
    T. C. Vijayaraghavan
    computational complexity, 2010, 19 : 57 - 98
  • [45] DESCRIPTIVE COMPLEXITY FOR COUNTING COMPLEXITY CLASSES
    Arenas, Marcelo
    Munoz, Martin
    Riveros, Cristian
    LOGICAL METHODS IN COMPUTER SCIENCE, 2020, 16 (01)
  • [46] Descriptive Complexity for Counting Complexity Classes
    Arenas, Marcelo
    Munoz, Martin
    Riveros, Cristian
    2017 32ND ANNUAL ACM/IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS), 2017,
  • [47] CLASSIFYING PROBLEMS ON LINEAR CONGRUENCES AND ABELIAN PERMUTATION GROUPS USING LOGSPACE COUNTING CLASSES
    Arvind, V.
    Vijayaraghavan, T. C.
    COMPUTATIONAL COMPLEXITY, 2010, 19 (01) : 57 - 98
  • [48] Descriptive complexity of list H-coloring problems in logspace: a refined dichotomy
    Dalmau, Victor
    Egri, Laszlo
    Hell, Pavol
    Larose, Benoit
    Rafiey, Arash
    2015 30TH ANNUAL ACM/IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE (LICS), 2015, : 487 - 498
  • [49] COMPARING COMPLEXITY CLASSES
    BOOK, RV
    JOURNAL OF COMPUTER AND SYSTEM SCIENCES, 1974, 9 (02) : 213 - 229
  • [50] Logics for complexity classes
    Naidenko, Vladimir
    LOGIC JOURNAL OF THE IGPL, 2014, 22 (06) : 1075 - 1093