The Experts below are selected from a list of 367896 Experts worldwide ranked by ideXlab platform
Amine Chaieb - One of the best experts on this subject based on the ideXlab platform.
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automated methods for formal proofs in simple Arithmetics and algebra
2008Co-Authors: Amine ChaiebAbstract:In an LCF-like theorem prover, any proof must be produced from a small set of inference rules. The development of automated proof methods in such systems is extremely important. In this thesis we study the following question: How should we integrate a proof procedure in an LCF-like theorem prover, both in general and in the special case of Arithmetics? We investigate three integration paradigms and present several proof procedures. These include universal and weak existential problems over rings, universal polynomial problems over the reals, quantifier elimination for parametric linear problems over ordered fields, Presburger arithmetic, mixed real-integer linear arithmetic, algebraically and real closed fields. Our work has been carried out in the Isabelle framework.
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Verifying mixed real-integer quantifier elimination
Lecture Notes in Computer Science, 2006Co-Authors: Amine ChaiebAbstract:We present a formally verified quantifier elimination procedure for the first order theory over linear mixed real-integer Arithmetics in higher-order logic based on a work by Weispfenning. To this end we provide two verified quantifier elimination procedures: for Presburger arithmitics and for linear real Arithmetics.
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IJCAR - Verifying mixed real-integer quantifier elimination
Automated Reasoning, 2006Co-Authors: Amine ChaiebAbstract:We present a formally verified quantifier elimination procedure for the first order theory over linear mixed real-integer Arithmetics in higher-order logic based on a work by Weispfenning. To this end we provide two verified quantifier elimination procedures: for Presburger arithmitics and for linear real Arithmetics.
Martin Stepnicka - One of the best experts on this subject based on the ideXlab platform.
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Arithmetics of extensional fuzzy numbers part i introduction
IEEE International Conference on Fuzzy Systems, 2012Co-Authors: Michal Holcapek, Martin StepnickaAbstract:Up to our best knowledge, distinct so far existing Arithmetics of fuzzy numbers, usually stemming from the Zadeh's extensional principle, do not preserve some of the important properties of the standard Arithmetics of classical (real) numbers. Obviously, although we cannot expect that a generalization of standard arithmetic will preserve precisely all its properties however, at least the most important ones should be preserved. We present a novel framework of Arithmetics of extensional fuzzy numbers that preserves more or less all the important (algebraic) properties of the arithmetic of real numbers and thus, seems to be an important seed for further investigations on this topic. The suggested approach Arithmetics of extensional fuzzy numbers is demonstrated on many examples and besides the algebraic properties, it is also shown that it carries some desirable practical properties.
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Arithmetics of extensional fuzzy numbers part ii algebraic framework
IEEE International Conference on Fuzzy Systems, 2012Co-Authors: Michal Holcapek, Martin StepnickaAbstract:In the first part of this contribution, we proposed extensional fuzzy numbers and a working arithmetic for them that may be abstracted to so-called many identities algebras (MI-algebras, for short). In this second part, we show that the proposed MI-algebras give a framework not only for the arithmetic of extensional fuzzy numbers, but also for other Arithmetics of fuzzy numbers and even more general sets of real vectors used in mathematical morphology. This entitles us to develop a theory of MI-algebras to study general properties of structures for which the standard algebras are not appropriate. Some of the basic concepts and properties are presented here.
Giorgio Delzanno - One of the best experts on this subject based on the ideXlab platform.
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Automatic verification of parameterized cache coherence protocols
Lecture Notes in Computer Science, 2000Co-Authors: Giorgio DelzannoAbstract:We propose a new method for the verification of parameterized cache coherence protocols. Cache coherence protocols are used to maintain data consistency in multiprocessor systems equipped with local fast caches. In our approach we use arithmetic constraints to model possibly infinite sets of global states of a multiprocessor system with many identical caches. In preliminary experiments using symbolic model checkers for infinite-state systems based on real Arithmetics (HyTech [HHW97] and DMC [DP99]) we have automatically verified safety properties for parameterized versions of widely implemented write-invalidate and write-update cache coherence policies like the Mesi, Berkeley, Illinois, Firefly and Dragon protocols [Han93]. With this application, we show that symbolic model checking tools originally designed for hybrid and concurrent systems can be applied successfully to a new class of infinite-state systems of practical interest.
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CAV - Automatic Verification of Parameterized Cache Coherence Protocols
Computer Aided Verification, 2000Co-Authors: Giorgio DelzannoAbstract:We propose a new method for the verification of parameterized cache coherence protocols. Cache coherence protocols are used to maintain data consistency in multiprocessor systems equipped with local fast caches. In our approach we use arithmetic constraints to model possibly infinite sets of global states of a multiprocessor system with many identical caches. In preliminary experiments using symbolic model checkers for infinite-state systems based on real Arithmetics (HyTech [HHW97] and DMC [DP99])) we have automatically verified safety properties for parameterized versions of widely implemented write-invalidate and write-update cache coherence policies like the Mesi, Berkeley, Illinois, Firefly and Dragon protocols [Han93]. With this application, we show that symbolic model checking tools originally designed for hybrid and concurrent systems can be applied successfully to a new class of infinite-state systems of practical interest.
Michal Holcapek - One of the best experts on this subject based on the ideXlab platform.
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Arithmetics of extensional fuzzy numbers part i introduction
IEEE International Conference on Fuzzy Systems, 2012Co-Authors: Michal Holcapek, Martin StepnickaAbstract:Up to our best knowledge, distinct so far existing Arithmetics of fuzzy numbers, usually stemming from the Zadeh's extensional principle, do not preserve some of the important properties of the standard Arithmetics of classical (real) numbers. Obviously, although we cannot expect that a generalization of standard arithmetic will preserve precisely all its properties however, at least the most important ones should be preserved. We present a novel framework of Arithmetics of extensional fuzzy numbers that preserves more or less all the important (algebraic) properties of the arithmetic of real numbers and thus, seems to be an important seed for further investigations on this topic. The suggested approach Arithmetics of extensional fuzzy numbers is demonstrated on many examples and besides the algebraic properties, it is also shown that it carries some desirable practical properties.
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Arithmetics of extensional fuzzy numbers part ii algebraic framework
IEEE International Conference on Fuzzy Systems, 2012Co-Authors: Michal Holcapek, Martin StepnickaAbstract:In the first part of this contribution, we proposed extensional fuzzy numbers and a working arithmetic for them that may be abstracted to so-called many identities algebras (MI-algebras, for short). In this second part, we show that the proposed MI-algebras give a framework not only for the arithmetic of extensional fuzzy numbers, but also for other Arithmetics of fuzzy numbers and even more general sets of real vectors used in mathematical morphology. This entitles us to develop a theory of MI-algebras to study general properties of structures for which the standard algebras are not appropriate. Some of the basic concepts and properties are presented here.
Javier Garrido - One of the best experts on this subject based on the ideXlab platform.
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Parametrizable Fixed-Point Arithmetic for HIL With Small Simulation Steps
IEEE Journal of Emerging and Selected Topics in Power Electronics, 2019Co-Authors: Alberto Sanchez, Angel De Castro, Javier GarridoAbstract:Hardware-in-the-loop (HIL) techniques are increasingly used for test purposes because of their advantages over classical simulations. Field-programmable gate arrays (FPGAs) are becoming popular in HIL systems because of their parallel computing capabilities. In most cases, FPGAs are mainly used for signal processing, such as input pulsewidth modulation sampling and conditioning, while there are also processors to model the system. However, there are other HIL systems that implement the model in the FPGA. For FPGA implementation and regarding the Arithmetics, there are two main possibilities: fixed-point and floating-point. Fixed-point is the best choice only when real-time simulations with small simulation steps are needed, while floating-point is the common choice because of its flexibility and ease of use. This paper presents a novel hybrid arithmetic for FPGAs called parametrizable fixed-point which takes advantage of both Arithmetics as the internal operations are accomplished using simple signed integers, while the point location of the variables can be adjusted as necessary without redesigning the model of the plant. The experimental results show that a buck converter can be modeled using this novel arithmetic with a simulation step below 20 ns. Besides, the experiments prove that the proposed model can be adjusted to any set of values (voltages, currents, capacitances, and so on.) keeping its accuracy without resynthesizing, showing the big advantage over the fixed-point arithmetic.
