1,582 research outputs found
Quantitative Model Checking of Linear-Time Properties Based on Generalized Possibility Measures
Model checking of linear-time properties based on possibility measures was
studied in previous work (Y. Li and L. Li, Model checking of linear-time
properties based on possibility measure, IEEE Transactions on Fuzzy Systems,
21(5)(2013), 842-854). However, the linear-time properties considered in the
previous work was classical and qualitative, possibility information of the
systems was not considered at all. We shall study quantitative model checking
of fuzzy linear-time properties based on generalized possibility measures in
the paper. Both the model of the system, as well as the properties the system
needs to adhere to, are described using possibility information to identify the
uncertainty in the model/properties. The systems are modeled by {\sl
generalized possibilistic Kripke structures} (GPKS, in short), and the
properties are described by fuzzy linear-time properties. Concretely, fuzzy
linear-time properties about reachability, always reachability, constrain
reachability, repeated reachability and persitence in GPKSs are introduced and
studied. Fuzzy regular safety properties and fuzzy regular properties
in GPKSs are introduced, the verification of fuzzy regular safety properties
and fuzzy regular properties using fuzzy finite automata are
thoroughly studied. It has been shown that the verification of fuzzy regular
safety properties and fuzzy regular properties in a finite GPKS can be
transformed into the verification of (always) reachability properties and
repeated reachability (persistence) properties in the product GPKS introduced
in this paper. Several examples are given to illustrate the methods presented
in the paper.Comment: arXiv admin note: text overlap with arXiv:1409.646
Model-Checking of Linear-Time Properties Based on Possibility Measure
We study the LTL model-checking in possibilistic Kripke structure using
possibility measure. First, the notion of possibilistic Kripke structure and
the related possibility measure are introduced, then model-checking of
reachability and repeated reachability linear-time properties in finite
possibilistic Kripke structure are studied. Standard safety property and
-regular property in possibilistic Kripke structure are introduced, the
verification of regular safety property and -regular property using finite
automata are thoroughly studied. It has been shown that the verification of
regular safety property and -regular property in finite possibilistic Kripke
structure can be transformed into the verification of reachability property and
repeated reachability property in the product possibilistic Kripke structure
introduced in this paper. Several examples are given to illustrate the methods
presented in the paper.Comment: 22pages,5 figure
Semi-dynamic shortest-path tree algorithms for directed graphs with arbitrary weights
Given a directed graph with arbitrary real-valued weights, the single
source shortest-path problem (SSSP) asks for, given a source in ,
finding a shortest path from to each vertex in . A classical SSSP
algorithm detects a negative cycle of or constructs a shortest-path tree
(SPT) rooted at in time, where are the numbers of edges and
vertices in respectively. In many practical applications, new constraints
come from time to time and we need to update the SPT frequently. Given an SPT
of , suppose the weight on a certain edge is modified. We show by
rigorous proof that the well-known {\sf Ball-String} algorithm for positively
weighted graphs can be adapted to solve the dynamic SPT problem for directed
graphs with arbitrary weights. Let be the number of vertices that are
affected (i.e., vertices that have different distances from or different
parents in the input and output SPTs) and the number of edges incident to
an affected vertex. The adapted algorithms terminate in
time, either detecting a negative cycle (only in the decremental case) or
constructing a new SPT for the updated graph. We show by an example that
the output SPT may have more than necessary edge changes to . To remedy
this, we give a general method for transforming into an SPT with minimal
edge changes in time provided that has no cycles with zero length.Comment: 27 pages, 3 figure
Exogenous Quantum Operator Logic Based on Density Operators
Although quantum logic by using exogenous approach has been proposed for
reasoning about closed quantum systems, an improvement would be worth to study
quantum logic based on density operators instead of unit vectors in the state
logic point of view. In order to achieve this, we build an exogenous quantum
operator logic(EQOL) based on density operators for reasoning about open
quantum systems. We show that this logic is sound and complete. Just as the
exogenous quantum propositional logic(EQPL), by applying exogenous approach,
EQOL is extended from the classical propositional logic, and is used to
describe the state logic based on density operators. As its applications, we
confirm the entanglement property about Bell states by reasoning and logical
argument, also verify the existence of eavesdropping about the basic BB84
protocol. As a novel type of mathematical formalism for open quantum systems,
we introduce an exogenous quantum Markov chain(EQMC) where its quantum states
are labelled using EQOL formulae. Then, an example is given to illustrate the
termination verification problem of a generalized quantum loop program
described using EQMC.Comment: 26 pages, 1 figure
Monogamy of th Power Entanglement Measurement in Qubit Systems
In this paper, we study the th power monogamy properties related to
the entanglement measure in bipartite states. The monogamy relations related to
the th power of negativity and the Convex- Roof Extended Negativity are
obtained for N-qubit states. We also give a tighter bound of hierarchical
monogamy inequality for the entanglement of formation. We find that the GHZ
state and W state can be used to distinguish the th power the
concurrence for . Furthermore, we compare concurrence with
negativity in terms of monogamy property and investigate the difference between
them.Comment: 6 pages, 2 figure
Quantitative Computation Tree Logic Model Checking Based on Generalized Possibility Measures
We study generalized possibilistic computation tree logic model checking in
this paper, which is an extension of possibilistic computation logic model
checking introduced by Y.Li, Y.Li and Z.Ma (2014). The system is modeled by
generalized possibilistic Kripke structures (GPKS, in short), and the verifying
property is specified by a generalized possibilistic computation tree logic
(GPoCTL, in short) formula. Based on generalized possibility measures and
generalized necessity measures, the method of generalized possibilistic
computation tree logic model checking is discussed, and the corresponding
algorithm and its complexity are shown in detail. Furthermore, the comparison
between PoCTL introduced in (2013) and GPoCTL is given. Finally, a thermostat
example is given to illustrate the GPoCTL model-checking method
Continuity in Information Algebras
In this paper, the continuity and strong continuity in domain-free
information algebras and labeled information algebras are introduced
respectively. A more general concept of continuous function which is defined
between two domain-free continuous information algebras is presented. It is
shown that, with the operations combination and focusing, the set of all
continuous functions between two domain-free s-continuous information algebras
forms a new s-continuous information algebra. By studying the relationship
between domain-free information algebras and labeled information algebras, it
is demonstrated that they do correspond to each other on s-compactness
On Quotients of Formal Power Series
Quotient is a basic operation of formal languages, which plays a key role in
the construction of minimal deterministic finite automata (DFA) and the
universal automata. In this paper, we extend this operation to formal power
series and systemically investigate its implications in the study of weighted
automata. In particular, we define two quotient operations for formal power
series that coincide when calculated by a word. We term the first operation as
(left or right) \emph{quotient}, and the second as (left or right)
\emph{residual}. To support the definitions of quotients and residuals, the
underlying semiring is restricted to complete semirings or complete
c-semirings. Algebraical properties that are similar to the classical case are
obtained in the formal power series case. Moreover, we show closure properties,
under quotients and residuals, of regular series and weighted context-free
series are similar as in formal languages. Using these operations, we define
for each formal power series two weighted automata and . Both weighted automata accepts , and is the minimal
deterministic weighted automaton of . The universality of is
justified and, in particular, we show that is a sub-automaton of
. Last but not least, an effective method to construct the
universal automaton is also presented in this paper.Comment: 48 pages, 3 figures, 30 conference
Relational reasoning in the region connection calculus
This paper is mainly concerned with the relation-algebraical aspects of the
well-known Region Connection Calculus (RCC). We show that the contact relation
algebra (CRA) of certain RCC model is not atomic complete and hence infinite.
So in general an extensional composition table for the RCC cannot be obtained
by simply refining the RCC8 relations. After having shown that each RCC model
is a consistent model of the RCC11 CT, we give an exhaustive investigation
about extensional interpretation of the RCC11 CT. More important, we show the
complemented closed disk algebra is a representation for the relation algebra
determined by the RCC11 table. The domain of this algebra contains two classes
of regions, the closed disks and closures of their complements in the real
plane.Comment: Latex2e, 35 pages, 2 figure
Coherent-induced state ordering with fixed mixedness
In this paper, we study coherence-induced state ordering with Tsallis
relative entropy of coherence, relative entropy of coherence and norm
of coherence. Firstly, we show that these measures give the same ordering for
single-qubit states with a fixed mixedness or a fixed length along the
direction . Secondly, we consider some special cases of high
dimensional states, we show that these measures generate the same ordering for
the set of high dimensional pure states if any two states of the set satisfy
majorization relation. Moreover, these three measures generate the same
ordering for all states with a fixed mixedness. Finally, we discuss
dynamics of coherence-induced state ordering under Markovian channels. We find
phase damping channel don't change the coherence-induced state ordering for
some single-qubit states with fixed mixedness, instead amplitude damping
channel change the coherence-induced ordering even though for single-qubit
states with fixed mixedness
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