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39
Algebraic Decision Diagrams and their Applications
, 1993
"... In this paper we present theory and experiments on the Algebraic Decision Diagrams (ADD's). These diagrams extend BDD's by allowing values from an arbitrary finite domain to be associated with the terminal nodes. We present a treatment founded in boolean algebras and discuss algorithms and results i ..."
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Cited by 263 (17 self)
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In this paper we present theory and experiments on the Algebraic Decision Diagrams (ADD's). These diagrams extend BDD's by allowing values from an arbitrary finite domain to be associated with the terminal nodes. We present a treatment founded in boolean algebras and discuss algorithms and results in applications like matrix multiplication and shortest path algorithms. Furthermore, we outline possible applications of ADD's to logic synthesis, formal verification, and testing of digital systems.
Two Classes of Boolean Functions for Dependency Analysis
 SCIENCE OF COMPUTER PROGRAMMING
, 1994
"... Many static analyses for declarative programming/database languages use Boolean functions to express dependencies among variables or argument positions. Examples include groundness analysis, arguably the most important analysis for logic programs, finiteness analysis and functional dependency analys ..."
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Cited by 66 (4 self)
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Many static analyses for declarative programming/database languages use Boolean functions to express dependencies among variables or argument positions. Examples include groundness analysis, arguably the most important analysis for logic programs, finiteness analysis and functional dependency analysis for databases. We identify two classes of Boolean functions that have been used: positive and definite functions, and we systematically investigate these classes and their efficient implementation for dependency analyses. On the theoretical side we provide syntactic characterizations and study the expressiveness and algebraic properties of the classes. In particular, we show that both are closed under existential quantification. On the practical side we investigate various representations for the classes based on reduced ordered binary decision diagrams (ROBDDs), disjunctive normal form, conjunctive normal form, Blake canonical form, dual Blake canonical form, and two forms specific to de...
Symmetry Detection and Dynamic Variable Ordering of Decision Diagrams
, 1996
"... Knowing that some variables are symmetric in a function has numerous applications; in particular, it can help produce better variable orders for Binary Decision Diagrams (BDDs) and related data structures (e.g., Algebraic Decision Diagrams). It has been observed that there often exists an optimum ..."
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Cited by 55 (2 self)
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Knowing that some variables are symmetric in a function has numerous applications; in particular, it can help produce better variable orders for Binary Decision Diagrams (BDDs) and related data structures (e.g., Algebraic Decision Diagrams). It has been observed that there often exists an optimum order for a BDD wherein symmetric variables are contiguous. We propose a new algorithm for the detection of symmetries, based on dynamic reordering, and we study its interaction with the reordering algorithm itself. We show that combining sifting with an efficient symmetry check for contiguous variables results in the fastest symmetry detection algorithm reported to date and produces better variable orders for many BDDs. The overhead on the sifting algorithm is negligible. 1
General Conditions for the Decomposition of State Holding Elements
 In International Symposium on Advanced Research in Asynchronous Circuits and Systems, Aizu
, 1996
"... A fundamental problem in the design of speedindependent asynchronous circuits is the decomposition or splitting up of highfanin operators into two or more lowerfanin operators. In this paper, we develop general techniques to decided whether a particular decomposition of an arbitrary stateholding ..."
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Cited by 32 (4 self)
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A fundamental problem in the design of speedindependent asynchronous circuits is the decomposition or splitting up of highfanin operators into two or more lowerfanin operators. In this paper, we develop general techniques to decided whether a particular decomposition of an arbitrary stateholding or combinational element into two elements with an isolated internal signal is correct. These techniques are extended to determine efficiently all legal decompositions in a parameterized family. 1 Introduction In this paper, we derive general conditions on the legality of decompositions in speedindependent circuits. The primary motivation for this work is the desire to implement asynchronous circuits generated using the Martin's synthesis methodology [8] in fixed fanin structures such as the Montage field programmable gate array [6]. The work described here differs significantly from previous work on the decomposition problem [1, 10]. Instead of performing decompositions into particular st...
Structural Methods for the Synthesis of SpeedIndependent Circuits
, 1996
"... Most existing tools for the synthesis of asynchronouscircuits from Signal Transition Graphs (STGs) derive the reachability graph for the calculation of logic equations. This paper presents novel methods exclusively based on the structural analysis of the underlying Petri net. This methodology can be ..."
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Cited by 19 (10 self)
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Most existing tools for the synthesis of asynchronouscircuits from Signal Transition Graphs (STGs) derive the reachability graph for the calculation of logic equations. This paper presents novel methods exclusively based on the structural analysis of the underlying Petri net. This methodology can be applied to any STG that can be covered by State Machines and, in particular, to all live and safe freechoice STGs. Significant improvements with regard to existing structural methods are provided. The new techniques have been implemented in an experimental tool that has been able to synthesize specificationswith over10 27 markings, some of them being nonfree choice. 1 Introduction Petri nets (PNs) are a powerful formalism to model concurrent systems. As a model, their most interesting feature is the capability of implicitly describing a vast state space by a succinct representation, which gracefully captures the notions of causality, concurrency and conflict between events. Petri nets...
Negative Boolean Constraints
, 1994
"... Systems of Boolean constraints which allow negative constraints such as f 6` g are investigated. The results form a basis for algorithms to determine satisfiability, validity, implication, equivalence and variable elimination for such systems. These algorithms have applications in spatial query deco ..."
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Cited by 19 (0 self)
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Systems of Boolean constraints which allow negative constraints such as f 6` g are investigated. The results form a basis for algorithms to determine satisfiability, validity, implication, equivalence and variable elimination for such systems. These algorithms have applications in spatial query decomposition, machine reasoning, and constraint logic programming. Proofs of the results rely on independence of inequations, which enables results for systems with a single inequation to be lifted to systems with many inequations. 1 Introduction Since Boole [2], systems (or conjunctions) of positive constraints f ` g over a Boolean algebra have been extensively studied. Here, we introduce and study a more general notion of Boolean constraint system in which negative Boolean constraints f 6` g are also allowed. Systems of positive and negative constraints have not yet been widely studied in their own right. This may be because in the case of twovalued Boolean algebras, negative constraints ad...
Semantic Forgetting in Answer Set Programming
, 2008
"... The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In t ..."
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Cited by 16 (4 self)
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The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In this paper, we establish a declarative theory of forgetting for disjunctive logic programs under answer set semantics that is fully based on semantic grounds. The suitability of this theory is justified by a number of desirable properties. In particular, one of our results shows that our notion of forgetting can be entirely captured by classical forgetting. We present several algorithms for computing a representation of the result of forgetting, and provide a characterization of the computational complexity of reasoning from a logic program under forgetting. As applications of our approach, we present a fairly general framework for resolving conflicts in inconsistent knowledge bases that are represented by disjunctive logic programs, and we show how the semantics of inheritance logic programs and update logic programs from the literature can be characterized through forgetting. The basic idea of the conflict resolution framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency. In particular, we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming.
ConstraintBased Query Optimization for Spatial Databases
 Proc. 10th ACM PODS
, 1991
"... We present a method for converting a system of multivariate Boolean constraints into a sequence of univariate range queries of the type supported by current spatial databases. The method relies on the transformation of a Boolean constraint system into triangular form. We extend previous results in t ..."
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Cited by 14 (1 self)
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We present a method for converting a system of multivariate Boolean constraints into a sequence of univariate range queries of the type supported by current spatial databases. The method relies on the transformation of a Boolean constraint system into triangular form. We extend previous results in this area by considering negative as well as positive constraints. We also present a method to approximate triangular Boolean constraints by bounding box constraints. 1 Introduction In spatial database systems, there is a gap between the highlevel query language required by applications and users, and the simpler query language supported by the underlying spatial datastructure. Typically, applications such as geographic information systems [5, 8, 10], visual language parsers [7], VLSI design rule checkers [14], require a query language in which queries and integrity constraints may be expressed over a number of variables subject to Boolean constraints (that is, constraints over sets). In ...
Structural methods to improve the symbolic analysis of Petri nets
 IN PROC. ICATPN '99, LNCS 1639
, 1999
"... Symbolic techniques based on BDDs (Binary Decision Diagrams) have emerged as an efficient strategy for the analysis of Petri nets. The existing techniques for the symbolic encoding of each marking use a fixed set of variables per place, leading to encoding schemes with very low density. This drawba ..."
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Cited by 14 (1 self)
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Symbolic techniques based on BDDs (Binary Decision Diagrams) have emerged as an efficient strategy for the analysis of Petri nets. The existing techniques for the symbolic encoding of each marking use a fixed set of variables per place, leading to encoding schemes with very low density. This drawback has been previously mitigated by using ZeroSuppressed BDDs, that provide a typical reduction of BDD sizes by a factor of two. Structural Petri net theory provides Pinvariants that help to derive more efficient encoding schemes for the BDD representations of markings. Pinvariants also provide a mechanism to identify conservative upper bounds for the reachable markings. The unreachable markings determined by the upper bound can be used to alleviate both the calculation of the exact reachability set and the scrutiny of properties. Such approach allows to drastically decrease the number of variables for marking encoding and reduce memory and CPU requirements significantly.