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Symbolic Boolean manipulation with ordered binarydecision diagrams
 ACM COMPUTING SURVEYS
, 1992
"... Ordered BinaryDecision Diagrams (OBDDS) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satmfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented as grap ..."
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Cited by 1036 (13 self)
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Ordered BinaryDecision Diagrams (OBDDS) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as satmfiability and equivalence straightforward. A number of operations on Boolean functions can be implemented
Symbolic Model Checking for Realtime Systems
 INFORMATION AND COMPUTATION
, 1992
"... We describe finitestate programs over realnumbered time in a guardedcommand language with realvalued clocks or, equivalently, as finite automata with realvalued clocks. Model checking answers the question which states of a realtime program satisfy a branchingtime specification (given in an ..."
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Cited by 578 (50 self)
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in an extension of CTL with clock variables). We develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates, without constructing the state space. For this purpose, we introduce a calculus on computation trees over realnumbered time. Unfortunately
Concept Logics with Function Symbols
, 1994
"... . Recently, concept logics have been proposed which allow one to incorporate algorithms for domain specific problem solving into the classical resolution principle. The domain specific knowledge can be expressed by using the (KLONE like) knowledge representation language ALC, and problems are encod ..."
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to the fact that in general Skolem function symbols are introduced when translating formulas with restricted quantifiers into constrained clauses. While satisfiability of ALCconstraints with function symbols is decidable, validity of such constraints turns out to be undecidable. 1 Introduction Deductive
Spectra with Only Unary Function Symbols
, 1997
"... The spectrum of a firstorder sentence is the set of cardinalities of its finite models. This paper is concerned with spectra of sentences over languages that contain only unary function symbols. In particular, it is shown that a set S of natural numbers is the spectrum of a sentence over the langua ..."
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Cited by 9 (1 self)
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The spectrum of a firstorder sentence is the set of cardinalities of its finite models. This paper is concerned with spectra of sentences over languages that contain only unary function symbols. In particular, it is shown that a set S of natural numbers is the spectrum of a sentence over
Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I
, 1960
"... this paper in L a T E Xpartly supported by ARPA (ONR) grant N000149410775 to Stanford University where John McCarthy has been since 1962. Copied with minor notational changes from CACM, April 1960. If you want the exact typography, look there. Current address, John McCarthy, Computer Science Depa ..."
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Cited by 457 (3 self)
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for the IBM 704. Next comes another way of describing computations with symbolic expressions, and finally we give a recursive function interpretation of flow charts. We hope to describe some of the symbolic computations for which LISP has been used in another paper, and also to give elsewhere some
On the Termination of Logic Programs with Function Symbols
 IN DOVIER, A., & SANTOS COSTA, V. (EDS.), PROC. OF THE 8TH INT
, 2012
"... Recently there has been an increasing interest in the bottomup evaluation of the semantics of logic programs with complex terms. The main problem due to the presence of functional symbols in the head of rules is that the corresponding ground program could be infinite and that finiteness of models a ..."
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Cited by 5 (2 self)
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Recently there has been an increasing interest in the bottomup evaluation of the semantics of logic programs with complex terms. The main problem due to the presence of functional symbols in the head of rules is that the corresponding ground program could be infinite and that finiteness of models
A practical decision procedure for arithmetic with function symbols
 Journal of the ACM
, 1979
"... ABSTRACT A practical procedure is presented for an extension of quantifierfree Presburger arithmetic that permits arbitrary unmterpreted predicate and function symbols This theory includes many of the formulas one tends to encounter in program venficatlon and is powerful enough to encode the semant ..."
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Cited by 70 (1 self)
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ABSTRACT A practical procedure is presented for an extension of quantifierfree Presburger arithmetic that permits arbitrary unmterpreted predicate and function symbols This theory includes many of the formulas one tends to encounter in program venficatlon and is powerful enough to encode
Function symbols in ASP: Overview and perspectives
 IN NMR – ESSAYS CELEBRATING ITS 30TH ANNIVERSARY
, 2011
"... Answer Set Programming (ASP) is a highly expressive language that is widely used for knowledge representation and reasoning in many application scenarios. Thanks to disjunction and negation, the language allows the use of nondeterministic definitions for modeling complex problems in computer scienc ..."
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science, in particular in Artificial Intelligence. Traditionally, ASP has often been used as a firstorder language without function symbols, similar to Datalog, in order to deal with finite structures only. More recently, also uninterpreted function symbols have been frequently considered in the setting
Information Theory and Statistics
, 1968
"... Entropy and relative entropy are proposed as features extracted from symbol sequences. Firstly, a proper Iterated Function System is driven by the sequence, producing a fractaMike representation (CSR) with a low computational cost. Then, two entropic measures are applied to the CSR histogram of th ..."
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Cited by 1805 (2 self)
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Entropy and relative entropy are proposed as features extracted from symbol sequences. Firstly, a proper Iterated Function System is driven by the sequence, producing a fractaMike representation (CSR) with a low computational cost. Then, two entropic measures are applied to the CSR histogram
The empirical case for two systems of reasoning
, 1996
"... Distinctions have been proposed between systems of reasoning for centuries. This article distills properties shared by many of these distinctions and characterizes the resulting systems in light of recent findings and theoretical developments. One system is associative because its computations ref ..."
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Cited by 669 (4 self)
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reflect similarity structure and relations of temporal contiguity. The other is “rule based” because it operates on symbolic structures that have logical content and variables and because its computations have the properties that are normally assigned to rules. The systems serve complementary functions
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