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13
ConSIT: A Fully Automated Conditioned Program Slicer
, 2003
"... This paper describes the first fully automated conditioned slicing system, C##SIT, detailing the theory that underlies it, its architecture and the way it combines symbolic execution, theorem proving and slicing technologies. The use of C##SIT is illustrated with respect to the applications of testi ..."
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Cited by 16 (3 self)
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This paper describes the first fully automated conditioned slicing system, C##SIT, detailing the theory that underlies it, its architecture and the way it combines symbolic execution, theorem proving and slicing technologies. The use of C##SIT is illustrated with respect to the applications of testing and comprehension. ### #####: Conditioned Slicing, program conditioning, slicing, symbolic execution, path analysis
Characteristic Properties of MajorantComputability over the Reals
 Proc. of CSL'98, LNCS, 1584
"... . Characteristic properties of majorantcomputable realvalued functions are studied. A formal theory of computability over the reals which satisfies the requirements of numerical analysis used in Computer Science is constructed on the base of the definition of majorantcomputability proposed in [13 ..."
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Cited by 5 (5 self)
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. Characteristic properties of majorantcomputable realvalued functions are studied. A formal theory of computability over the reals which satisfies the requirements of numerical analysis used in Computer Science is constructed on the base of the definition of majorantcomputability proposed in [13]. A modeltheoretical characterization of majorantcomputability realvalued functions and their domains is investigated. A theorem which connects the graph of a majorantcomputable function with validity of a finite formula on the set of hereditarily finite sets on IR, HF( IR) (where IR is a proper elementary enlargement of the standard reals) is proven. A comparative analysis of the definition of majorantcomputability and the notions of computability earlier proposed by Blum et al., Edalat, Sunderhauf, PourEl and Richards, StoltenbergHansen and Tucker is given. Examples of majorantcomputable realvalued functions are presented. 1 Introduction In the recent time, attention to the prob...
Program Comprehension Assisted by Slicing and Transformation
"... Program slicing is a technique for program simplification based upon the deletion of statements which cannot affect the values of a chosen set of variables. Because slicing extracts a subcomponent of the program concerned with some specific computation on a set of variables, it can be used to assist ..."
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Cited by 5 (1 self)
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Program slicing is a technique for program simplification based upon the deletion of statements which cannot affect the values of a chosen set of variables. Because slicing extracts a subcomponent of the program concerned with some specific computation on a set of variables, it can be used to assist program comprehension, allowing a programmer to remodularise a program according to arbitrarily selected slicing criteria. In this paper it is shown that the simplification power of slicing can be improved if the syntactic restriction to statement deletion is removed, allowing slices to be constructed using any simplifying transformation which preserves the effect of the original program upon the set of variables of interest. It is also shown that quasi static slicing, first proposed by Venkatesh (and defined here in a slightly more general form), is the most suitable slicing paradigm for program comprehension. The various forms of slice are formally defined, an algorithm, based upon transformation, symbolic execution and conventional slicing is introduced for computing syntactically unrestricted, quasi static slices. A worked example is used to show howthis approach supports program comprehension by case analysis and simplification.
Constructibility and Decidability versus Domain Independence and Absoluteness
"... We develop a unified framework for dealing with constructibility and absoluteness in set theory, decidability of relations in effective structures (like the natural numbers), and domain independence of queries in database theory. Our framework and results suggest that domainindependence and absolut ..."
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Cited by 4 (2 self)
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We develop a unified framework for dealing with constructibility and absoluteness in set theory, decidability of relations in effective structures (like the natural numbers), and domain independence of queries in database theory. Our framework and results suggest that domainindependence and absoluteness might be the key notions in a general theory of constructibility, predicativity, and computability. 1
Formalisation of Computability of Operators and RealValued Functionals via Domain Theory
 Proceedings of CCA2000
"... Based on an eective theory of continuous domains, notions of computability for operators and realvalued functionals dened on the class of continuous functions are introduced. Denability and semantic characterisation of computable functionals are given. Also we propose a recursion scheme which is a ..."
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Cited by 3 (3 self)
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Based on an eective theory of continuous domains, notions of computability for operators and realvalued functionals dened on the class of continuous functions are introduced. Denability and semantic characterisation of computable functionals are given. Also we propose a recursion scheme which is a suitable tool for formalisation of complex systems, such as hybrid systems. In this framework the trajectories of continuous parts of hybrid systems can be represented by computable functionals. 1
Semantic Characterisations of Secondorder Computability Over the Real Numbers
 LNCS
, 2001
"... We propose semantic characterisations of secondorder computability over the reals based on denability theory. Notions of computability for operators and realvalued functionals dened on the class of continuous functions are introduced via domain theory. We consider the reals with and without equal ..."
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Cited by 2 (2 self)
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We propose semantic characterisations of secondorder computability over the reals based on denability theory. Notions of computability for operators and realvalued functionals dened on the class of continuous functions are introduced via domain theory. We consider the reals with and without equality and prove theorems which connect computable operators and realvalued functionals with validity of nite formulas. 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 ..."
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Cited by 2 (1 self)
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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
Generalised Computability and an Application to Hybrid Systems
 LNCS
, 2001
"... We investigate the concept of generalised computability of operators and functionals dened on the set of continuous functions, rstly introduced in [9]. By working in the reals, with equality and without equality, we study properties of generalised computable operators and functionals. Also we pr ..."
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Cited by 1 (1 self)
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We investigate the concept of generalised computability of operators and functionals dened on the set of continuous functions, rstly introduced in [9]. By working in the reals, with equality and without equality, we study properties of generalised computable operators and functionals. Also we propose an interesting application to formalisation of hybrid systems. We obtain some class of hybrid systems, which trajectories are computable in the sense of computable analysis.
The Uniformity Principle for Σdefinability with Applications to Computable Analysis
"... This work is the next step in a series of papers [3, 4] using arguments from definability theory to logically characterise computable continuous data. In order to do this we have proposed the notion of majorantcomputability and developed logical approach to computability over continuous data. This ..."
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Cited by 1 (1 self)
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This work is the next step in a series of papers [3, 4] using arguments from definability theory to logically characterise computable continuous data. In order to do this we have proposed the notion of majorantcomputability and developed logical approach to computability over continuous data. This approach is based on representations of continuous data by suitable structures without the equality test and Σdefinability in extensions of the structures by hereditarily finite sets. One of the main features of the notion of majorantcomputability is that on the one side it is independent from concrete representations of the elements of structures on the other side it is flexible, i.e. we can change the language of Σformulas to express appropriate computability properties. In this talk we introduce and study the language of ΣKformulas which is an extension of the language of Σformulas. This language simplifies reasoning about computability of higher type continuous data, and admits elimination of universal quantifiers bounded by computable compact sets. In order to show these properties we prove Uniformity principle for Σdefinability over the real
A New Approach to Computability on Real Numbers
, 1997
"... We introduce majorant computability of functions on reals. A structural theorem is proved, which connects the graph of a majorantcomputable function with validity of a finite formula on the set of the hereditarily finite set HF( ¯ R) (where ¯ R is an elementary proper extension of standard real nu ..."
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We introduce majorant computability of functions on reals. A structural theorem is proved, which connects the graph of a majorantcomputable function with validity of a finite formula on the set of the hereditarily finite set HF( ¯ R) (where ¯ R is an elementary proper extension of standard real numbers). The class of majorantcomputable functions in our approach include an interesting class of real total functions having meromorphic extension on C. This class in particular contains functions which are solutions of known differential equations. The notion of a majorantcomputable functional on the set of total majorantcomputable real functions is defined. As an example of a majorantcomputable functional the Riemann integral is proposed. 1 Section 1. Introduction Section 1 Introduction The semiring of natural numbers is the classical structure for which the concept of computability has been defined and studied rather well. Though several definitions were independently proposed,...