Showing papers on "Disjunctive normal form published in 1987"

Learning Decision Lists

Abstract: This paper introduces a new representation for Boolean functions, called decision lists, and shows that they are efficiently learnable from examples. More precisely, this result is established for k-;DL – the set of decision lists with conjunctive clauses of size k at each decision. Since k-DL properly includes other well-known techniques for representing Boolean functions such as k-CNF (formulae in conjunctive normal form with at most k literals per clause), k-DNF (formulae in disjunctive normal form with at most k literals per term), and decision trees of depth k, our result strictly increases the set of functions that are known to be polynomially learnable, in the sense of Valiant (1984). Our proof is constructive: we present an algorithm that can efficiently construct an element of k-DL consistent with a given set of examples, if one exists.

A DNF without regular shortest consensus path

Abstract: A disjunctive normal form without regular shortest consensus path is given. The question Tseitin asked in 1968 and Gaul mentioned again in 1977 is answered.

An Extended Disjunctive Normal Form Approach for Optimizing Recursive Logic Queries in Loosely Coupled Environments

Abstract: We present an approach to processing logic queries in loosely coupled environments. We emphasize the importance of the loose coupling technique as a practkal solution to provide deductive capabiities to existing DBMS+especially when an efficient access to a very large database is required in the. process of inferencing. We propose the Extended Disjunctive Normal Form (EDNF) as the basis of our approach. The EDNF is an extension of the disjunctive normal form of relational algebra expressions so as to include recursion. The EDNF is well suited for a loosely coupled environment, where an existing DBMS and optimiition can be fully exploited. It also serves as a clear, graphical characterixation of various recursions that can occur in logic queries. We first present the basic form of the EDNF and then use it as a building block to process a more general class of queries. We extend valid usage of Clark% negation-as-failure evaluation technique to incorporate negation for most practical situations. We also propose new criteria for safety and termination in the presence of negation. To the extent of the authors’ knowledge, optimixation in loosely coupled environments has not been seriously addressed in previous research. We believe our technique provides significant progress in this dhection.

Fast, Small, and Static Combinatorial CMOS Circuits

Abstract: We present ALPS, a new way to generate layout from boolean equations. We use an original tree-structured representation of arbitrary boolean expressions, more compact than classic disjunctive form, allowing fast symbolic manipulation and natural mapping onto silicon. This implementation of ALPS produces static CMOS layout using a cascode-switch style. We present measurements done on fabricated circuits. For a large class of functions, particularly semi-regular control logic, VLSI layout generated by ALPS compares favorably in speed and area to PLAS and Standard-Cell designs.

Using Decision Trees to Derive the Complement of a Binary Function with Multiple-Valued Inputs

Abstract: An algorithm to minimize decision trees of Boolean functions with multiple-valued inputs is presented. The recursive algorithm is used to obtain a complement of a sum-of-products expression for a binary function with multiple-valued inputs. In the case where each input is p-valued, the algorithm produces at most pn−l products for n-variable functions, whereas Sasao's algorithm produces pn/2 products. This upper bound on the number of products is the best possible.

The mechanisms of temporal inference

Abstract: The properties of a temporal language are determined by its constituent elements: the temporal objects which it can represent, the attributes of those objects, the relationships between them, the axioms which define the default relationships, and the rules which define the statements that can be formulated. The methods of inference which can be applied to a temporal language are derived in part from a small number of axioms which define the meaning of equality and order and how those relationships can be propagated. More complex inferences involve detailed analysis of the stated relationships. Perhaps the most challenging area of temporal inference is reasoning over disjunctive temporal constraints. Simple forms of disjunction do not sufficiently increase the expressive power of a language while unrestricted use of disjunction makes the analysis NP-hard. In many cases a set of disjunctive constraints can be converted to disjunctive normal form and familiar methods of inference can be applied to the conjunctive sub-expressions. This process itself is NP-hard but it is made more tractable by careful expansion of a tree-structured search space.

Disjoint disjunctive form of boolean functions and its applications

Abstract: Due to upscaling of digital systems, the development of efficient representations and manipulating algorithms of Boolean functions is becoming increasingly important. This paper considers the representation by the disjoint disjunctive form from representations of Boolean functions, and describes the properties, characteristics and manipulating algorithms. Conventionally used sharp operation and disjoint sharp operation are made more efficient for the algorithm which generates disjoint disjunctive forms. Moreover, a binary tree method is proposed as a method which generates disjoint disjunctive forms of positive and negative functions simultaneously. This binary tree method is also very powerful as a method to obtain negation of logical formulas, and is five to ten times faster than the conventional one using disjoint sharp operation in a case of 10-variable function. Also, for the problem of number of product terms, which is generally regarded as a shortcoming of the disjoint disjunctive form, we conduct further studies by considering the simplest disjoint disjunctive form. Moreover, we show a unique negation algorithm as an example of using the properties of the disjoint disjunctive form more aggressively.