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The Quantitative LinearTime–BranchingTime Spectrum
"... We present a distanceagnostic approach to quantitative verification. Taking as input an unspecified distance on system traces, or executions, we develop a gamebased framework which allows us to define a spectrum of different interesting system distances corresponding to the given trace distance. T ..."
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We present a distanceagnostic approach to quantitative verification. Taking as input an unspecified distance on system traces, or executions, we develop a gamebased framework which allows us to define a spectrum of different interesting system distances corresponding to the given trace distance. Thus we extend the classic lineartime–branchingtime spectrum to a quantitative setting, parametrized by trace distance. We also provide fixedpoint characterizations of all system distances, and we prove a general transfer principle which allows us to transfer counterexamples from the qualitative to the quantitative setting, showing that all system distances are mutually topologically inequivalent.
General quantitative specification theories with modalities
 Juhani Karhumäki, Arto Lepistö, and Michail Prilutskii, editors, CSR, volume 7353 of LNCS
, 2012
"... Abstract. This paper proposes a new theory of quantitative specifications. It generalizes the notions of stepwise refinement and compositional design operations from the Boolean to an arbitrary quantitative setting. It is shown that this general approach permits to recast many existing problems wh ..."
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Cited by 5 (4 self)
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Abstract. This paper proposes a new theory of quantitative specifications. It generalizes the notions of stepwise refinement and compositional design operations from the Boolean to an arbitrary quantitative setting. It is shown that this general approach permits to recast many existing problems which arise in system design. 1
Topological (Bi)Simulation
 Electronic Lecture Notes in Computer Science
, 2002
"... Since the work of van Glabbeek [9]... In this paper we define the notion of a labelled topological transition system, i.e., a labelled transition system where the state space is structured using a topology. Then, we define topological simulation and topological bisimulation. These notions extend the ..."
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Cited by 2 (1 self)
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Since the work of van Glabbeek [9]... In this paper we define the notion of a labelled topological transition system, i.e., a labelled transition system where the state space is structured using a topology. Then, we define topological simulation and topological bisimulation. These notions extend the traditional ones by considering not only single steps but arbitrary long (accumulating) sequences of steps in the transfer (zigzag) conditions. We prove that these topological notions are a preorder and an equivalence respectively and that they are stronger than the nontopological notions. We also prove that they are topological notions (invariant under the application of continuous transition morphisms)
Noname manuscript No. (will be inserted by the editor) A Generalized GleasonPierceWard Theorem
, 2009
"... Abstract The GleasonPierceWard theorem gives constraints on the divisor and field size of a linear divisible code over a finite field whose dimension is half of the code length. This result is a departure point for the study of selfdual codes. In recent years, additive codes have been studied int ..."
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Abstract The GleasonPierceWard theorem gives constraints on the divisor and field size of a linear divisible code over a finite field whose dimension is half of the code length. This result is a departure point for the study of selfdual codes. In recent years, additive codes have been studied intensively because of their use in additive quantum codes. In this work, we generalize the GleasonPierceWard theorem on linear codes over GF (q), q = p m, to additive codes over GF (q). The first step of our proof is an application of a generalized upper bound on the dimension of a divisible code determined by its weight spectrum. The bound is proved by Ward for linear codes over GF (q), and is generalized by Liu to any code as long as the MacWilliams identities are satisfied. The trace map and an analogous homomorphism x ↦ → x − x p on GF (q) are used to complete our proof. Keywords additive codes · GleasonPierceWard theorem · divisible codes · Ward’s bound