Security and privacy with K-step opacity for finite automata via a novel algebraic approach

2021 ◽  
pp. 014233122110403
Author(s):  
Qian Xu ◽  
Zhipeng Zhang ◽  
Yongyi Yan ◽  
Chengyi Xia
Keyword(s):  
Formal Language ◽  
Polynomial Matrix ◽  
Finite Automata ◽  
Algebraic Approach ◽  
Security And Privacy ◽  
Related Area ◽  
Physical Systems ◽  
The Matrix ◽  
Problem Description ◽  
Necessary And Sufficient

As an important secretive attribute, opacity of cyber-physical systems (CPSs) has attracted considerable attention. Existing works on opacity mainly concentrate on the formal language method by assuming that the intruder tracks partial knowledge of observable transitions. In this paper, under the framework of Boolean semi-tensor product (BSTP) of matrix, we extend the verification of opaque property to algebraic mechanisms that have great advantages in problem description and solution. First, we show that how [Formula: see text]-step opacity problem of nondeterministic finite automata (NFAs) can be transformed to the construction problem of a polynomial matrix that characterizes the state estimation eavesdropped by malicious intruders within the last [Formula: see text] observations. Second, the necessary and sufficient condition of verifying [Formula: see text]-step opacity is obtained, which is equivalent to validate the composition of elements within the polynomial matrix. Finally, the effectiveness of this result is demonstrated by an illustrative example. Taking together, the matrix-based method will be useful to deliver a novel theoretical tool for investigating the privacy-preserving problem in the related area of CPSs.

Observability analysis of combined finite automata based upon semi-tensor product of matrices approach

2020 ◽  
pp. 014233122097252
Author(s):  
Zengqiang Chen ◽  
Yingrui Zhou ◽  
Zhipeng Zhang ◽  
Zhongxin Liu
Keyword(s):  
Tensor Product ◽  
Finite Automata ◽  
Initial State ◽  
Algebraic Form ◽  
Incidence Matrices ◽  
Observability Analysis ◽  
Current State ◽  
The Matrix ◽  
Problem Description ◽  
Product Of Matrices

As a fundamental subject, the state estimation of deterministic finite automata has received considerable attention. Especially, it is increasingly necessary to study various problems based on more complex systems. In this paper, the observability of three kinds of combining automata, structured in parallel, serial and feedback manners, are investigated based on an algebraic state space approach. Compared with the formal language method, the matrix approach has great advantages in problem description and solution. Because of inconsistent frameworks of these combined automata, we optimize structure matrices by pseudo-commutation of semi-tensor product and power-reducing matrix. In addition, we construct corresponding incidence matrices by labelling to avoid superfluous null elements in the logical matrix occupying storage space. It follows that the observability analysis could be carried out under two polynomial matrices, established from the above algebraic form. Meanwhile, two algorithms, judging whether a combined automaton is initial state observable or current state observable, are presented. Finally, there are two representative examples to actualize our approach.

Da eine oder mehrere betroffen …

2020 ◽  
Vol 48 (1) ◽  
pp. 47-100
Author(s):  
Melitta Gillmann
Keyword(s):  
High Frequency ◽  
Formal Language ◽  
Subordinate Clause ◽  
Matrix Clause ◽  
Very High Frequency ◽  
Corpus Study ◽  
Causal Relations ◽  
Legal Texts ◽  
The Matrix ◽  
Very High

AbstractBased on a corpus study conducted using the GerManC corpus (1650–1800), the paper sketches the functional and sociosymbolic development of subordinate clause constructions introduced by the subjunctor da ‘since’ in different text genres. In the second half of the 17th and the first half of the 18th century, the da clauses were characterized by semantic vagueness: Besides temporal, spatial and causal relations, the subjunctor established conditional, concessive, and adversative links between clauses. The corpus study reveals that different genres are crucial to the readings of da clauses. Spatial and temporal usages, for example, occur more often in sermons than in other genres. The conditional reading, in contrast, strongly tends to occur in legal texts, where it displays very high frequency. This could be the reason why da clauses carry indexical meaning in contemporary German and are associated with formal language. Over the course of the 18th century, the causal usages increase in all genres. Surprisingly, these causal da clauses tend to be placed in front of the matrix clause despite the overall tendency of causal clauses to follow the matrix clause.

scholarly journals Complex-analytic and matrix-analytic solutions for a queueing system with group service controlled by arrivals

2000 ◽  
Vol 13 (4) ◽  
pp. 415-427
Author(s):  
Lev Abolnikov ◽  
Alexander Dukhovny
Keyword(s):  
Block Size ◽  
Iteration Process ◽  
Analytic Solutions ◽  
Analytic Method ◽  
Service Time Distribution ◽  
Matrix Analytic Method ◽  
Queueing Process ◽  
The Matrix ◽  
Matrix Iteration ◽  
Necessary And Sufficient

A bulk M/G/1 system is considered that responds to large increases (decreases) of the queue during the service act by alternating between two service modes. The switching rule is based on two “up” and “down” thresholds for total arrivals over the service act. A necessary and sufficient condition for the ergodicity of a Markov chain embedded into the main queueing process is found. Both complex-analytic and matrix-analytic solutions are obtained for the steady-state distribution. Under the assumption of the same service time distribution in both modes, a combined complex-matrix-analytic method is introduced. The technique of “matrix unfolding” is used, which reduces the problem to a matrix iteration process with the block size much smaller than in the direct application of the matrix-analytic method.

scholarly journals On circulant codes with prescribed distances

1977 ◽  
Vol 16 (3) ◽  
pp. 361-369
Author(s):  
M. Deza ◽  
Peter Eades
Keyword(s):  
Sufficient Conditions ◽  
Difference Sets ◽  
Necessary And Sufficient Conditions ◽  
Necessary Condition ◽  
Weighing Matrices ◽  
Cyclic Difference Sets ◽  
The Matrix ◽  
Circulant Codes ◽  
Necessary And Sufficient ◽  
Square Matrix

Necessary and sufficient conditions are given for a square matrix to te the matrix of distances of a circulant code. These conditions are used to obtain some inequalities for cyclic difference sets, and a necessary condition for the existence of circulant weighing matrices.

scholarly journals SEF4CPSIoT Software Engineering Framework for Cyber-Physical and IoT Systems

2021 ◽  
Vol 5 (1) ◽  
pp. 1-24
Author(s):  
Muthu Ramachandran
Keyword(s):  
Software Engineering ◽  
Smart Home ◽  
Cyber Physical Systems ◽  
Classification Model ◽  
Security And Privacy ◽  
Physical Systems ◽  
Iot Applications ◽  
Communications Technologies ◽  
Efficient Control ◽  
Efficient Integration

Cyber-physical systems (CPS) have emerged to address the need for more efficient integration of modern advancement in cyber and wireless communications technologies such as 5G with physical objects. In addition, CPSs systems also needed to efficient control of security and privacy when we compare them with internet of things (IoT). In recent years, we experienced lack of security concerns with smart home IoT applications such as home security camera, etc. Therefore, this paper proposes a systematic software engineering framework for CPS and IoT systems. This paper also proposed a comprehensive requirements engineering framework for CPS-IoT applications which can also be specified using BPMN modelling and simulation to verify and validate CPS-IoT requirements with smart contracts. In this context, one of the key contribution of this paper is the innovative and generic requirements classification model for CPS-IoT application services, and this can also be applied to other emerging technologies such as fog, edge, cloud, and blockchain computing.

scholarly journals On Solutions of the Matrix Equation A ∘ l X  = B with respect to M M -2 Semitensor Product

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Jin Wang
Keyword(s):  
Matrix Equation ◽  
Matrix Multiplication ◽  
Sufficient Condition ◽  
Mathematical Tool ◽  
Necessary And Sufficient Condition ◽  
The Matrix ◽  
Necessary And Sufficient

M M -2 semitensor product is a new and very useful mathematical tool, which breaks the limitation of traditional matrix multiplication on the dimension of matrices and has a wide application prospect. This article aims to investigate the solutions of the matrix equation A ° l X = B with respect to M M -2 semitensor product. The case where the solutions of the equation are vectors is discussed first. Compatible conditions of matrices and the necessary and sufficient condition for the solvability is studied successively. Furthermore, concrete methods of solving the equation are provided. Then, the case where the solutions of the equation are matrices is studied in a similar way. Finally, several examples are given to illustrate the efficiency of the results.

The algebra of differential forms on a full matric bialgebra

1993 ◽  
Vol 114 (1) ◽  
pp. 111-130 ◽  
Author(s):  
A. Sudbery
Keyword(s):  
Vector Space ◽  
Commutative Algebra ◽  
Differential Algebra ◽  
Differential Forms ◽  
Sufficient Conditions ◽  
Classical Case ◽  
Algebra Of Functions ◽  
The Matrix ◽  
Constant Coefficients ◽  
Necessary And Sufficient

AbstractWe construct a non-commutative analogue of the algebra of differential forms on the space of endomorphisms of a vector space, given a non-commutative algebra of functions and differential forms on the vector space. The construction yields a differential bialgebra which is a skew product of an algebra of functions and an algebra of differential forms with constant coefficients. We give necessary and sufficient conditions for such an algebra to exist, show that it is uniquely determined by the differential algebra on the vector space, and show that it is a non-commutative superpolynomial algebra in the matrix elements and their differentials (i.e. that it has the same dimensions of homogeneous components as in the classical case).

On the factorable spaces of absolutely p-summable, null, convergent, and bounded sequences

2021 ◽  
Vol 71 (6) ◽  
pp. 1375-1400
Author(s):  
Feyzi Başar ◽  
Hadi Roopaei
Keyword(s):  
Lower Bound ◽  
Sequence Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Matrix Transformations ◽  
Infinite Matrix ◽  
The Matrix ◽  
Alpha Beta ◽  
Necessary And Sufficient ◽  
Bounded Sequences

Abstract Let F denote the factorable matrix and X ∈ {ℓp , c 0, c, ℓ ∞}. In this study, we introduce the domains X(F) of the factorable matrix in the spaces X. Also, we give the bases and determine the alpha-, beta- and gamma-duals of the spaces X(F). We obtain the necessary and sufficient conditions on an infinite matrix belonging to the classes (ℓ p (F), ℓ ∞), (ℓ p (F), f) and (X, Y(F)) of matrix transformations, where Y denotes any given sequence space. Furthermore, we give the necessary and sufficient conditions for factorizing an operator based on the matrix F and derive two factorizations for the Cesàro and Hilbert matrices based on the Gamma matrix. Additionally, we investigate the norm of operators on the domain of the matrix F. Finally, we find the norm of Hilbert operators on some sequence spaces and deal with the lower bound of operators on the domain of the factorable matrix.

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