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11.
在一些特殊领域中需要建立一定的实验环境对软件性能进行测试,因此实验环境与实际环境之间的近似程度对软件的性能起到关键作用。为建立环境之间的近似度量,在进程代数理论基础上,根据软件与环境的交互程度,利用拓扑度量和论域理论中的偏序关系,建立实验环境之间近似程度的量化模型。根据软件与环境之间的部分交互,建立实验环境之间近似程度的度量模型。通过实例对度量模型进行说明,并证明度量模型的代数性质。 相似文献
12.
借助软集合,提出了格蕴涵代数的软LI-理想的概念,研究了软集运算下的一些诸如交、且等基本性质,并给出了格蕴涵代数的软LI-理想的一些等价刻画。此外,研究了格蕴涵代数的软LI-理想与格蕴涵代数的软格理想之间的关系。得到了格蕴涵代数的软LI-理想像与原像的性质。 相似文献
13.
14.
粗糙集的信息观和代数观是通过不同的方式来定义知识的,两种观点在绝对约简中完全等价,但是在相对约简中,两种观点的关系并不明确。文章研究了两种观点在相对约简中的关系,证明了两种观点在相容决策表中完全相同,而在不相容决策表中,信息观的现有定理存在错误,也就是说信息观不适用于不相容决策表。 相似文献
15.
Recently, Aceto, Fokkink and Ingólfsdóttir proposed an algorithm to turn any sound and ground-complete axiomatisation of any preorder listed in the linear time-branching time spectrum at least as coarse as the ready simulation preorder, into a sound and ground-complete axiomatisation of the corresponding equivalence—its kernel. Moreover, if the former axiomatisation is ω-complete, so is the latter. Subsequently, de Frutos Escrig, Gregorio Rodríguez and Palomino generalised this result, so that the algorithm is applicable to any preorder at least as coarse as the ready simulation preorder, provided it is initials preserving. The current paper shows that the same algorithm applies equally well to weak semantics: the proviso of initials preserving can be replaced by other conditions, such as weak initials preserving and satisfying the second τ-law. This makes it applicable to all 87 preorders surveyed in “the linear time-branching time spectrum II” that are at least as coarse as the ready simulation preorder. We also extend the scope of the algorithm to infinite processes, by adding recursion constants. As an application of both extensions, we provide a ground-complete axiomatisation of the CSP failures equivalence for BCCS processes with divergence. 相似文献
16.
Automatic Construction and Verification of Isotopy Invariants 总被引:1,自引:0,他引:1
Volker Sorge Andreas Meier Roy McCasland Simon Colton 《Journal of Automated Reasoning》2008,40(2-3):221-243
We extend our previous study of the automatic construction of isomorphic classification theorems for algebraic domains by
considering the isotopy equivalence relation. Isotopism is an important generalisation of isomorphism, and is studied by mathematicians in domains
such as loop theory. This extension was not straightforward, and we had to solve two major technical problems, namely, generating
and verifying isotopy invariants. Concentrating on the domain of loop theory, we have developed three novel techniques for
generating isotopic invariants, by using the notion of universal identities and by using constructions based on subblocks.
In addition, given the complexity of the theorems that verify that a conjunction of the invariants form an isotopy class,
we have developed ways of simplifying the problem of proving these theorems. Our techniques employ an interplay of computer
algebra, model generation, theorem proving, and satisfiability-solving methods. To demonstrate the power of the approach,
we generate isotopic classification theorems for loops of size 6 and 7, which extend the previously known enumeration results.
This work was previously beyond the capabilities of automated reasoning techniques.
The author’s work was supported by EPSRC MathFIT grant GR/S31099. 相似文献
17.
We describe the design, implementation and experimental evaluation of new algorithms for computing the approximate factorization of multivariate polynomials with complex coefficients that contain numerical noise. Our algorithms are based on a generalization of the differential forms introduced by W. Ruppert and S. Gao to many variables, and use singular value decomposition or structured total least squares approximation and Gauss–Newton optimization to numerically compute the approximate multivariate factors. We demonstrate on a large set of benchmark polynomials that our algorithms efficiently yield approximate factorizations within the coefficient noise even when the relative error in the input is substantial (10−3). 相似文献
18.
Feng Feng Young Bae Jun 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2009,13(11):1113-1121
The notion of an inductive semimodule over an ordered *-semiring is introduced and some related properties are investigated.
Inductive semimodules are extensions of several important algebraic structures such as Kleene modules, Kleene algebras and
inductive *-semirings. We prove that an inductive semimodule over an ordered *-semiring K is a Kleene module if and only if K is a Kleene algebra. Moreover, we establish that the vector module of an inductive semimodule over an ordered Conway semiring
is again an inductive semimodule over the matrix semiring. Consequently, in an inductive semimodule over an ordered Conway
semiring, least solutions to linear inequation systems can be denoted by linear expressions, avoiding the least fixed point
operator. In addition, we also introduce a related notion called weak inductive semimodules, and propose several open problems
on them.
相似文献
Young Bae JunEmail: |
19.
Pre-/postconditions have been extensively used in program specification, e.g. Z [Spi89], VDM [Jon86], and proof, e.g. Hoare logic, Dijkstra's guarded commands [DiF88]. In [ScP86, SPB90] the authors introduced neutral and central relations to formalise the concept of the rest stays the same. In this paper we abstract away from the specific definition of neutral relation given in [SPB90], through the mechanism of relational boolean algebras. This leads to the definition of implicitly central relations which are easier for the user in practical examples and facilitate the use of pre-/postcondition reasoning about truly concurrent behaviour. 相似文献
20.
This paper presents a bicoprime factorization (BCF) approach to deal with various stability problems for linear discrete time-varying (LTV) systems within the framework of nest algebra. Based on the bicoprime factorization, we give necessary and sufficient conditions for (strongly) simultaneous stabilization of three systems, which generalize similar results for systems by coprime factorization (CF). Finally, when the bicoprime factorization for the plant and controller has additive perturbations, we derive sufficient conditions using the norm inequality for robust stability of the system. 相似文献