Results 1  10
of
10
An Efficient Algorithm for Computing Bisimulation Equivalence
 Theor. Comput. Sci
, 2004
"... In this paper we propose an ecient algorithmic solution to the problem of determining a Bisimulation Relation on a nite structure working both on the explicit and on the implicit (symbolic) representation. As far as the explicit case is concerned, starting from a settheoretic point of view we ..."
Abstract

Cited by 34 (3 self)
 Add to MetaCart
In this paper we propose an ecient algorithmic solution to the problem of determining a Bisimulation Relation on a nite structure working both on the explicit and on the implicit (symbolic) representation. As far as the explicit case is concerned, starting from a settheoretic point of view we propose an algorithm that optimizes the solution to the Relational Coarsest Partition Problem given by Paige and Tarjan in 1987; its use in modelchecking packages is discussed and tested. For well structured graphs our algorithm reaches a linear worstcase behaviour. The same ideas can be elaborated for the development of the algorithm for the symbolic case.
G.: A uniform approach to constraintsolving for lists, multisets, compact lists, and sets
 ACM Trans. Comput. Log
, 2008
"... Lists, multisets, and sets are wellknown data structures whose usefulness is widely recognized in various areas of Computer Science. They have been analyzed from an axiomatic point of view with a parametric approach in [Dovier et al. 1998] where the relevant unification algorithms have been develop ..."
Abstract

Cited by 9 (5 self)
 Add to MetaCart
Lists, multisets, and sets are wellknown data structures whose usefulness is widely recognized in various areas of Computer Science. They have been analyzed from an axiomatic point of view with a parametric approach in [Dovier et al. 1998] where the relevant unification algorithms have been developed. In this paper we extend these results considering more general constraints, namely equality and membership constraints and their negative counterparts.
Combining sets with cardinals
 J. of Automated Reasoning
"... Abstract. We introduce a quantifierfree settheoretic language for combining sets with elements in the presence of the cardinality operator. We prove that the language is decidable by providing a combination method specifically tailored to the combination domain of sets, cardinal numbers, and eleme ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
Abstract. We introduce a quantifierfree settheoretic language for combining sets with elements in the presence of the cardinality operator. We prove that the language is decidable by providing a combination method specifically tailored to the combination domain of sets, cardinal numbers, and elements. Our method uses as black boxes a decision procedure for the elements and a decision procedure for cardinal numbers. To be correct, our method requires that the theory of elements be stably infinite. However, we show that if we restrict set variables to range over finite sets only, then it is possible to modify our method so that it works even when the theory of the elements is not stably infinite. 1.
A New Approach to Predicative Set Theory
"... We suggest a new basic framework for the WeylFeferman predicativist program by constructing a formal predicative set theory PZF which resembles ZF. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an a ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
We suggest a new basic framework for the WeylFeferman predicativist program by constructing a formal predicative set theory PZF which resembles ZF. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an absolute way, independent of the extension of the “surrounding universe”. This idea is implemented using syntactic safety relations between formulas and sets of variables. These safety relations generalize both the notion of domainindependence from database theory, and Godel notion of absoluteness from set theory. The language of PZF is typefree, and it reflects real mathematical practice in making an extensive use of statically defined abstract set terms. Another important feature of PZF is that its underlying logic is ancestral logic (i.e. the extension of FOL with a transitive closure operation). 1
Threevariable statements of setpairing
 Theoretical Computer Science
"... The approach to algebraic specifications of set theories proposed by Tarski and Givant inspires current research aimed at taking advantage of the purely equational nature of the resulting formulations for enhanced automation of reasoning on aggregates of various kinds: sets, bags, hypersets, etc. Th ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
The approach to algebraic specifications of set theories proposed by Tarski and Givant inspires current research aimed at taking advantage of the purely equational nature of the resulting formulations for enhanced automation of reasoning on aggregates of various kinds: sets, bags, hypersets, etc. The viability of the said approach rests upon the possibility to form ordered pairs and to decompose them by means of conjugated projections. Ordered pairs can be conceived of in many ways: along with the most classic one, several other pairing functions are examined, which can be preferred to it when either the axiomatic assumptions are too weak to enable pairing formation à la Kuratowski, or they are strong enough to make the specification of conjugated projections particularly simple, and their formal properties easy to check within the calculus of binary relations.
From Set Unification to Set Constraints
 IL MILIONE: A JOURNEY IN THE COMPUTATIONAL LOGIC IN ITALY
"... In this paper, we briefly summarize some of the most challenging issues that arise when allowing sets to be dealt with as firstclass objects in a logic language, ranging from set unification of wellfounded and nonwellfounded sets to set constraint solving. ..."
Abstract
 Add to MetaCart
In this paper, we briefly summarize some of the most challenging issues that arise when allowing sets to be dealt with as firstclass objects in a logic language, ranging from set unification of wellfounded and nonwellfounded sets to set constraint solving.
FORMATIVE PROCESSES WITH APPLICATIONS TO THE DECISION PROBLEM IN SET THEORY: II. POWERSET AND SINGLETON OPERATORS, FINITENESS PREDICATE ∗
, 2008
"... This research has been partially funded by PRIN project 2006/2007 ‘Largescale development of certified mathematical proofs’. 1 2 In this paper we solve the satisfiability problem for a quantifierfree fragment of set theory involving the powerset and the singleton operators and a finiteness predica ..."
Abstract
 Add to MetaCart
This research has been partially funded by PRIN project 2006/2007 ‘Largescale development of certified mathematical proofs’. 1 2 In this paper we solve the satisfiability problem for a quantifierfree fragment of set theory involving the powerset and the singleton operators and a finiteness predicate, besides the basic Boolean set operators of union, intersection, and difference. The more restricted fragment obtained by dropping the finiteness predicate has been shown to have a solvable satisfiability problem in a previous paper, by establishing for it a small model property. To deal with the finiteness predicate we have formulated and proved a small model witness property for our fragment of set theory, namely a property which asserts that any satisfiable formula of our fragment has a model admitting a “small” representation. Key words Satisfiability decision problem, satisfaction algorithm, ZermeloFraenkel set theory. 3 1
of MultiLevel Syllogistic with the Cartesian
"... A decision procedure for a twosorted extension ..."