Topic
BIT predicate
About: BIT predicate is a research topic. Over the lifetime, 7 publications have been published within this topic receiving 24 citations. The topic is also known as: Ackermann coding.
Papers
2 Jul 1999
TL;DR: The ordered conjecture on BIT-structures can be translated to the problem of comparing the expressive power of FO and LFP in the context of finite set theory and the advantage of this approach is that it can use set-theoretic concepts and methods to identify certain fragments of LFP for which the restriction of the ordered conjecture is already hard to settle, as well as other restricted fragments that actually collapse to FO.
Abstract: The ordered conjecture states that least fixed-point logic LFP is strictly more expressive than first-order logic FO on every infinite class of ordered finite structures. It has been established that either way of settling this conjecture would resolve open problems in complexity theory. In fact, this holds true even for the particular instance of the ordered conjecture on the class of BIT-structures, that is, ordered finite structures with a built-in BIT predicate. Using a well known isomorphism from the natural numbers to the hereditarily finite sets that maps BIT to the membership relation between sets, the ordered conjecture on BIT-structures can be translated to the problem of comparing the expressive power of FO and LFP in the context of finite set theory. The advantage of this approach is that we can use set-theoretic concepts and methods to identify certain fragments of LFP for which the restriction of the ordered conjecture is already hard to settle, as well as other restricted fragments of LFP that actually collapse to FO. These results advance the state of knowledge about the ordered conjecture on BIT-structures and contribute to the delineation of the boundary where this conjecture becomes hard to settle.
10 citations
TL;DR: With Ehrenfeucht-Fraisse games, it is proved that @D"1@D"0 on BFR, which implies @D @D 0 on B FR, and thus solve an open problem raised by Albert Atserias in his dissertation.
9 citations
4 Mar 1999
TL;DR: In this article, the authors show that a variant of Greibach's "hardest context-free language" is LOGCFL-complete under quantifier-free BIT-free interpretations.
Abstract: Building upon the known generalized-quantifier-based firstorder characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory relating monoidal quantifiers to NC1 and its subclasses. In the absence of the BIT predicate, we resolve the main issues: we show in particular that no single outermost unary groupoidal quantifier with FO can capture all the context-free languages, and we obtain the surprising result that a variant of Greibach's "hardest contextfree language" is LOGCFL-complete under quantifier-free BIT-free interpretations. We then prove that FO with unary groupoidal quantifiers is strictly more expressive with the BIT predicate than without. Considering a particular groupoidal quantifier, we prove that first-order logic with majority of pairs is strictly more expressive than first-order with majority of individuals. As a technical tool of independent interest, we define the notion of an aperiodic nondeterministic finite automaton and prove that FO translations are precisely the mappings computed by single-valued aperiodic nondeterministic finite transducers.
6 citations
21 Aug 2000
TL;DR: It is shown that the iteration of a positive bounded formula converges in polylogarithmically many steps in the cardinality of the structure, which provides a natural characterization of the complexity class consisting of all languages computable by bounded-depth, polynomial-size circuits, andpolylogarity-time uniformity.
Abstract: We investigate the complexity of the fixed-points of bounded formulas in the context of finite set theory; that is, in the context of arbitrary classes of finite structures that are equipped with a built-in BIT predicate, or equivalently, with a built-in membership relation between hereditarily finite sets (input relations are allowed). We show that the iteration of a positive bounded formula converges in polylogarithmically many steps in the cardinality of the structure. This extends a previously known much weaker result. We obtain a number of connections with the rudimentary languages and deterministic polynomial-time. Moreover, our results provide a natural characterization of the complexity class consisting of all languages computable by bounded-depth, polynomial-size circuits, and polylogarithmic-time uniformity. As a byproduct, we see that this class coincides with LH(P), the logarithmic-time hierarchy with an oracle to deterministic polynomial-time. Finally, we discuss the connection of this result with the well-studied algorithms for integer division.
1 citations
Patent•
27 Mar 2014
TL;DR: In this paper, an apparatus and method for executing instructions using a predicate register is described, where the predicate register stores a set of predicate condition bits, the predicate condition bit specifies whether results of a particular predicated instruction sequence are to be retained or discarded, and predicate execution logic is used to execute a first predicate instruction to indicate a start of a new predicate instruction sequence.
Abstract: An apparatus and method are described for executing instructions using a predicate register. For example, one embodiment of a processor comprises: a register set including a predicate register to store a set of predicate condition bits, the predicate condition bits specifying whether results of a particular predicated instruction sequence are to be retained or discarded; and predicate execution logic to execute a first predicate instruction to indicate a start of a new predicated instruction sequence by copying a condition value from a processor control register in the register set to the predicate register. In a further embodiment, the predicate condition bits in the predicate register are to be shifted in response to the first predicate instruction to free space within the predicate register for the new condition value associated with the new predicated instruction sequence.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2014 | 1 |
| 2008 | 1 |
| 2000 | 1 |
| 1999 | 2 |
| 1998 | 1 |
| 1992 | 1 |