Characterizations of parallel complexity classes

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1986

OSTI ID:7245029

Venkateswaran, H

A new two-person pebble game that abstracts the control structure of many parallel algorithms is defined and studied. This game extends the two-person pebble game defined by Dymond and Tompa (JCSS, Vol. 30, no.2, 1985, pp. 149-161) in two ways: (a) the game is played on a Boolean circuit rather than on an unlabeled graph, and takes into consideration the types of the gates in the circuit, and (b) the two players' roles are completely symmetric. The new game is used to study the relationship between two natural parallel complexity classes, namely LOGCFL and AC/sup 1/. LOGCFL is the class of languages log space reducible to context-free languages. AC/sup 1/ is the class of languages accepted by an alternating Turning machine in space O(log n) and alternation depth O(log n). LOGCFL is a subclass of AC/sup 1/, but it is not known whether the inclusion is proper. For many problems in LOGCFL the algorithms that show their membership in that class also show their membership in AC/sup 1/. However, these algorithms do not use the full power of AC/sup 1/ computations. The two-person game defined here provides a model of computation in which this perceived difference can be quantified. This is done by characterizing the two classes using the same measures of resources in the game model.

• Research Organization: Washington Univ., Seattle (USA)
• OSTI ID: 7245029
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990210* -- Supercomputers-- (1987-1989)
ALGORITHMS
CONTROL THEORY
ELECTRONIC CIRCUITS
GATING CIRCUITS
MATHEMATICAL LOGIC
PARALLEL PROCESSING
PROGRAMMING
PROGRAMMING LANGUAGES