A novel type of Automata for dynamic, heterogeneous and random architectures
AA novel type of Automata for dynamic,heterogeneous and random architectures
Weijun ZHU
School of Information Engineering, Zhengzhou University, Zhengzhou, 450001, ChinaE-mail: [email protected]
July 21, 2018
Abstract
In this paper, the author aims to establish a mathematical model fora mimic computer. To this end, a novel automaton is proposed. First, aone-dimensional cellular automaton is used for expressing some dynamicchanges in the structure of a computing unit, a sequential automaton isemployed to describe some state transitions, a hierarchical automaton isemployed to express the different granularities of some computing units,and a probabilistic automaton is used to depict some random changes ofa computing unit. Second, the new automaton is obtained by combiningthe various types of automata mentioned above in the certain logical rela-tionship. To the best of our knowledge, the new automaton model is thefirst automaton which can portray the operation semantics for a mimiccomputing system, and it can directly describe some behaviors of a mimiccomputer.
Key words: mimic computing; automata theory; dynamic; heteroge-neous; random
It is well known that the Turing machine and many automata establish mathe-matical models for all kinds of computer systems in traditional computing. Thevon Neumann architecture solves the engineering and practical problems of theabove computational theory [1]. However, with the continuous development ofhigh-performance computers, power consumption is becoming one of the biggeststumbling block. In order to solve this problem, the high-efficiency computingtechnique has become a popular way of development of high-performance com-puters [1].China developed the world’s first prototype of mimic computers under theleadership of Academician Wu Jiangxing in September 2013 [2]. ”Mimic com-puting aim to obtain the essence of the high-efficiency computing through the1 a r X i v : . [ c s . F L ] M a r ultidimensional-reconstruction-based functional (mimic variety) architecture.”[1] ”It aims to improve efficiency of running by applying the idea that the appli-cation determines the structure and the structure determines the performance,as well as by timely dynamic reconstructing the corresponding systemic struc-ture or environment in execution.” The test results from a third-party show thatthe ratio of the efficiency of mimic computing raise 13.6-315 times on more than500 scenarios of web service, N-body and image recognition [2].As far as automaton theory is concerned, it has been proposed for somedecades. The early studies on automata provide a mathematical model whichportrays some systemic behaviors, for the different computing systems whichhave the different expressive abilities. What is more, these studies also providesa theoretical basis and a formal tool for the development of compilers. In recentyears, various automata have been applied to model checking and formal ver-ification. And these automata have been widely used in a series of fields suchas CPU design, network protocol verification, security protocol verification andsoftware engineering analysis.As for Mimic Computing (MC), none of the existing automata can establisha formal model of mimic computers. We need a model and method of automata.Motivated by it, a new automaton called Mimic Automaton (MA) is presentedin this paper. On this basis, a formal model of mimic computing is established.Furthermore, a Mimic Model Checking (MMC) method is proposed for MimicFormal Verifications (MFV). In addition, the MMC can be expected to detectsome malwares on mimic computers. These are the contributions of this paper. The definition of a mimic automaton is based on the Sequential Automata (SA)[3][4], Celluar Automata (CA) [5], Probabilistic Cellular Automata (PCA) [6]and Hierarchical Automata (HA) [3]. No more details on the definitions of thesetypes of automata are given here due to the limitation of space.
Definition 2.1 (Mimic Automata, (MA))
A mimic automaton A is a six-tuple ( A HA , γ, A SA , C, A CA , SA ↔ CA ) , where • A HA is a set of HA ; • γ is a set of Composition Functions; • A SA is a set of SA ; • C is a set of configurations of HA ; • A CA is a set of CA ; • SA ↔ CA determines the following two ways of combination between SA and CA . And these two ways can recursively call each other. ) use SA to express CA ( SA ← CA ) , we have Φ onestep r = f inal ( δ ) , where Φ onestep means one step of the running of CA , f inal ( δ ) means one running of SA , and r = denotes that the step of the running of CA consume the same timewith the running of SA .2) use CA to express SA ( SA → CA ) ,we have δ onestep r = f inal (Φ) , where δ onestep means one step of the running of SA , f inal (Φ) means one running of CA , and r = denotes that the step of the running of SA consume the same timewith the running of CA . From the definition 2.1, a mimic automaton is composed of sequential au-tomata, cellular automata and hierarchical automata according to some certainlogical relations, where sequential automata express state transitions, cellularautomata express dynamic heterogeneity (dynamic reconstruction of executionbody), hierarchical automata express granularity (different granularity of exe-cution bodies and different levels of state transitions).If a cellular automaton is replaced by a random cellular automaton, it candescribe the stochastic dynamic reconstruction of execution body. Therefore,a mimic automaton mathematically describes the state transitions in dynamic,heterogeneous and random architectures at different granularities. In otherwords, the combination of sequential automata, cellular automata, random cel-lular automata and hierarchical automata makes a mimic automaton show thecharacteristics of the mimic variants. It should be note that the core propertiesand characteristics of mimic computing are dynamic, heterogeneous, randomand the mimic variants.
A mimic automaton is employed to construct the formal model for DynamicalHeterogeneous Redundant (DHR) structure in this section. And DHR structureis the core architecture of network space mimic defense [7].A DHR structure is illustrated in the left subfigure of Figure 1. The DHRstructure can be modeled using the one-dimensional cellular automata in amimic automaton, as shown in the right subfigure of Figure 1. In this figure,the scheduling algorithm schedules a number of execution bodies in the way ofdynamical reconstruction, which perform some computational tasks. The rela-tionship between the DHR structure and a cellular automata is summarized asfollows: a cell unit of the automaton represent an execution bodies, the transi-tion function Φ of the automaton represent the scheduling algorithm, See Figure1 for more details.By using cellular automata to express the dynamic DHR structures, onecan use a mimic automaton to formally describe the computation of the exe-cution body in the following way: (1) The current state of a cell in a cellularautomaton corresponds to a sequential automaton in a hierarchy of a hierarchi-cal automaton; (2) the input of the DHR structure corresponds to the input of3igure 1: An one-dimensional cellular automaton for modeling a DHR structurethe sequential automaton; (3) the output of the DHR structure corresponds tothe output of the sequential automaton. It should be noted that, the state ofthe cellular automaton remains constant throughout the run of the sequentialautomaton.In a more complex DHR structure, different DHRs may be organized in alogical relationship. The left part of Figure 2 shows an example. Comparedwith the left part of Figure 1, the left part of Figure 2 is composed of thetwo serial DHR structures. The C sub-tree and C sub-tree in the right partof Figure 2 establish the formal model for the above two DHRs, respectively.And the components in the first three levels from top to down of the rightpart of Figure 2 describe the serially sequential relationship between the twoDHRs. The SA and the CA are nested with each other in two layers, as shownin the right part of Figure 2. In the inside nest, one-time runing of the SAcorresponds to a state transition of the CA. In contrast, one-time running ofthe CA corresponds to a state transition of the SA in the outside nest. Inthis example, the HA describes the different granularities, the CA describes thedynamic reconstruction of the execution bodies at a given granularity, and theSA describes the state transitions under the circumstance of a given granularityand a given execution body. A mimic automaton which is composed of theabove three types of automata establishes a formal model for a complex DHRstructure in this way. 4igure 2: A mimic automaton for modeling a complex DHR structure There are many studies which deal with SA model checking, CA model checking,HA model checking or PA model checking, such as [8], [9], [10], [11] and [12].Therefore, the general idea about the MA model checking is gotten, by dividingit into the above four kinds of model checking, as shown in Figure 3. No moredetails are given here due to the limitation of space.
In classical computing, the model checking technique has been employed to de-tect the malwares [13]. In comparison, the mimic model checking technique canbe also applied to Mimic Malware Detection (MMD) on some mimic computers.The principle of a MMD algorithm is depicted in Figure 4.
The new automaton, i.e., mimic automaton, can be employed to establish apreliminary formal model for mimic computing. With this tool at hand, one5igure 3: A flow diagram of MA model checkingFigure 4: The principle of a MMD algorithm6an artificially, semi-artificially or automatically conduct formal analysis formimic computing systems. This is a prospect of the application of this work.
Acknowledgements
This work has been supported by the Natural Science Foundation of Chinaunder Grant No.U1204608 as well as China Postdoctoral Science Foundationunder Grant No.2012M511588 and No.2015M572120.
References [1] Jiangxing WU, Meaning Mimic Computing Mimic Security Defense[J],Telecommunications Science, 2014, 30(7):1-7. (in Chinese)[2] Jiangxing WU, Mimic Computing & Mimic Security [EB/OL],http: // wenku.baidu.com //