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Fast probabilistic algorithms for verification of polynomial identities
 J. ACM
, 1980
"... ABSTRACT The starthng success of the RabmStrassenSolovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a wgorous ..."
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Cited by 533 (1 self)
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wgorous search for probabdisuc algonthms In dlustratmn of this observaUon, vanous fast probabdlsttc algonthms, with probability of correctness guaranteed a prion, are presented for testing polynomial ldentmes and propemes of systems of polynomials. Ancdlary fast algorithms for calculating resultants
Verification of polynomial system solvers
 In Proceedings of AWFS 2007
, 2007
"... Abstract. We discuss the verification of mathematical software solving polynomial systems symbolically by way of triangular decomposition. Standard verification techniques are highly resource consuming and apply only to polynomial systems which are easy to solve. We exhibit a new approach which mani ..."
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Cited by 9 (8 self)
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Abstract. We discuss the verification of mathematical software solving polynomial systems symbolically by way of triangular decomposition. Standard verification techniques are highly resource consuming and apply only to polynomial systems which are easy to solve. We exhibit a new approach which
The knowledge complexity of interactive proof systems
 in Proc. 27th Annual Symposium on Foundations of Computer Science
, 1985
"... Abstract. Usually, a proof of a theorem contains more knowledge than the mere fact that the theorem is true. For instance, to prove that a graph is Hamiltonian it suffices to exhibit a Hamiltonian tour in it; however, this seems to contain more knowledge than the single bit Hamiltonian/nonHamiltoni ..."
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Cited by 1267 (42 self)
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. Introduction. It is often regarded that saying a language L is in NP (that is, acceptable in nondeterministic polynomial time) is equivalent to saying that there is a polynomial time "proof system " for L. The proof system we have in mind is one where on input x, a "prover " creates a
On the complexity of . . . polynomial systems
, 2007
"... In this paper we present algorithmic and complexity results for polynomial sign evaluation over two real algebraic numbers, and for real solving of bivariate polynomial systems. Our main tool is signed polynomial remainder sequences; we exploit recent advances in univariate root isolation as well as ..."
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Cited by 1 (0 self)
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In this paper we present algorithmic and complexity results for polynomial sign evaluation over two real algebraic numbers, and for real solving of bivariate polynomial systems. Our main tool is signed polynomial remainder sequences; we exploit recent advances in univariate root isolation as well
Models and issues in data stream systems
 IN PODS
, 2002
"... In this overview paper we motivate the need for and research issues arising from a new model of data processing. In this model, data does not take the form of persistent relations, but rather arrives in multiple, continuous, rapid, timevarying data streams. In addition to reviewing past work releva ..."
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Cited by 770 (19 self)
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relevant to data stream systems and current projects in the area, the paper explores topics in stream query languages, new requirements and challenges in query processing, and algorithmic issues.
On solving parametric polynomial systems
"... triangular decomposition, regular chain. Abstract. Border polynomial and discriminant variety are two important notions related to parametric polynomial system solving, in particular, for partitioning the parameter values into regions where the solutions of the system depend continuously on the para ..."
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Cited by 1 (1 self)
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triangular decomposition, regular chain. Abstract. Border polynomial and discriminant variety are two important notions related to parametric polynomial system solving, in particular, for partitioning the parameter values into regions where the solutions of the system depend continuously
Random Sparse Polynomial Systems
, 2000
"... Let f :=(f 1 ; : : : ; f n ) be a sparse random polynomial system. This means that each f i has xed support (list of possibly nonzero coe cients) and each coecient has a Gaussian probability distribution of arbitrary variance. We express the expected number of roots of f inside a region U a ..."
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Cited by 5 (2 self)
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Let f :=(f 1 ; : : : ; f n ) be a sparse random polynomial system. This means that each f i has xed support (list of possibly nonzero coe cients) and each coecient has a Gaussian probability distribution of arbitrary variance. We express the expected number of roots of f inside a region U
SIS: A System for Sequential Circuit Synthesis
, 1992
"... SIS is an interactive tool for synthesis and optimization of sequential circuits. Given a state transition table, a signal transition graph, or a logiclevel description of a sequential circuit, it produces an optimized netlist in the target technology while preserving the sequential inputoutput b ..."
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Cited by 514 (41 self)
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SIS is an interactive tool for synthesis and optimization of sequential circuits. Given a state transition table, a signal transition graph, or a logiclevel description of a sequential circuit, it produces an optimized netlist in the target technology while preserving the sequential inputoutput behavior. Many different programs and algorithms have been integrated into SIS, allowing the user to choose among a variety of techniques at each stage of the process. It is built on top of MISII [5] and includes all (combinational) optimization techniques therein as well as many enhancements. SIS serves as both a framework within which various algorithms can be tested and compared, and as a tool for automatic synthesis and optimization of sequential circuits. This paper provides an overview of SIS. The first part contains descriptions of the input specification, STG (state transition graph) manipulation, new logic optimization and verification algorithms, ASTG (asynchronous signal transition graph) manipulation, and synthesis for PGA’s (programmable gate arrays). The second part contains a tutorial example illustrating the design process using SIS.
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 574 (50 self)
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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 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, many standard program properties, such as response for all nonzeno execution sequences (during which time diverges), cannot be characterized by fixpoints: we show that the expressiveness of the timed calculus is incomparable to the expressiveness of timed CTL. Fortunately, this result does not impair the symbolic verification of "implementable" realtime programsthose whose safety...
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