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Boundedwidth polynomialsize branching programs recognize exactly those languages
 in NC’, in “Proceedings, 18th ACM STOC
, 1986
"... We show that any language recognized by an NC ’ circuit (fanin 2, depth O(log n)) can be recognized by a width5 polynomialsize branching program. As any boundedwidth polynomialsize branching program can be simulated by an NC ’ circuit, we have that the class of languages recognized by such prog ..."
Abstract

Cited by 213 (13 self)
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We show that any language recognized by an NC ’ circuit (fanin 2, depth O(log n)) can be recognized by a width5 polynomialsize branching program. As any boundedwidth polynomialsize branching program can be simulated by an NC ’ circuit, we have that the class of languages recognized by such programs is exactly nonuniform NC’. Further, following
TWISTED LINKING NUMBERS VIA REPRESENTATIONS OF FUNDAMENTAL GROUPS
"... Using representations of fundamental groups, we introduce the concept of twistedlinking numbers. If the corresponding representation is trivial, the twistedlinking number coincides with the linking number. In the case of a nontrivial representation, however, this is not necessarily true, which impli ..."
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Using representations of fundamental groups, we introduce the concept of twistedlinking numbers. If the corresponding representation is trivial, the twistedlinking number coincides with the linking number. In the case of a nontrivial representation, however, this is not necessarily true, which implies that the twistedlinking number can detect the nontriviality of an embedding of S1. An example is given for which the linking number is trivial but the twistedlinking number is not. 1. Introduction. A linking number is an invariant of an oriented 2component link. Linking numbers are frequently used to study Alexander polynomials of knots and links, and coverings of certain spaces such as the complement of a knot or the complement of a link. There are several definitions of linking numbers,
1 Algebraic Semantics Based Behavioural Views of Configuration Relocation in Reconfigurable Computing
"... Abstract. The square cells specified by Ruby language, called Ruby cells, can be relocated by either rotation, horizontal flip, vertical flip or shifting in a regular array structure such as FPGA (Field Programmable Gate Array) or Cell Matrix�. In this paper, the behaviours of those relocations have ..."
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Abstract. The square cells specified by Ruby language, called Ruby cells, can be relocated by either rotation, horizontal flip, vertical flip or shifting in a regular array structure such as FPGA (Field Programmable Gate Array) or Cell Matrix�. In this paper, the behaviours of those relocations have been shown at two different levels, namely architectural level and logic level. In other words, the behavioural views describe the function of the configuration relocation of the target circuits regardless of its implementation. Under the behavioural view of configuration relocation at architectural level, the cell relocations can be specified and reasoned formally by algebraic laws of Ruby algebra and Group theory to create an abstract description of the configuration relocations of the target circuit without reference to particular elements within the reconfiguration device. Under the behavioural view of configuration relocation at logic level, the above abstract description considered as a Partial Orderbased Model (POM) and its dependencies are given by the transition relation and this is our approach to synthesise the algorithm for reconfiguration microcontroller automatically the information formalised in the highlevel specification languages.