Информационная безопасность: Материалы VI...
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3.docVI 2004
A.G. Chefranov
Turkish Republic of North Cyprus, Gazimagusa, Eastern Mediterranean University,
On approach to decision making formalization
1. Decisions are made on the base of consideration of information concerning desired query. Queries are formulated on the base of internal demands and demands of external world. Usual way of decision making is based on divide and conquer strategy: problem is split in sub problems which are considered similarly to initial problem unless it is decomposed in simply realizable parts. For instance, such approach is used in structured programming [1], unified modeling language (UML) [2], etc. However, this decomposition process is assumed to be made by humans, it is not automated in general case. Nowadays computers are not able to do such a work because they are based on low-level universal strategy of their behavior: infinite loop in which next instruction pointed by Program Counter register is fetched, analyzed and executed. Such a strategy requires sufficiently complicated Control Unit and means of interpretation (Arithmetic-Logic Unit), but it results in powerful computers which are widely in the use now after introducing of high and super-high level programming languages (Fortran, C, Database Management Systems, CAD-systems, etc). Such computers can run sufficiently complicated programs, can transform high-level programs in lower-level (compilers), can generate complicated codes on the base of descriptions of models (unified modeling language), but they are not able to respond on not known in advance demands of external and internal world. However, computer systems similarly to other natural creatures are affected by external world and they should be able to resist attempts of making harm to them and to repair themselves in the cases of failures. Currently, when each enterprise is linked via Internet to all others, and information stealing is widely spread (banking enterprises, for example), viruses can corrupt systems, behavior of computer systems is just similar to the fight of live creatures for survival. But contrary to the live creatures having adequate mechanisms for making their decisions in not friendly environment, computer systems cant live autonomously without participation of humans (programmers, administrators, managers, etc.). Even automated explorers of Mars (Pathfinder [3], nowadays, Spirit [4] and Opportunity) are controlled and repaired by humans remotely. Ideally, problems of safety of computer systems should be in their own responsibility. But for these purposes such systems need in well-developed mechanisms of making decisions, which could help them to find appropriate solutions (find source of error, way of problem decomposition, generation of respective codes, etc.).
2. Lets consider possible approach to formalization of making decisions process, activated by some query of arbitrary nature. This query should be analyzed to determine its parts. It may happen that part of query is understood by our system, and part is not understandable. Understandable means that respective notions are already known to system and it may relevantly interpret required: it knows respective data types, applicable to them operations, properties and so on. Not understandable part may include not previously used notions, or same as previously used terms but in some other meaning. Similar situation appears when translation is made from one language to the other: sense of one and the same word depends on its context and may differ significantly from usual meaning. Such additional information may be queried to the global bank of information (for example, Internet search servers: Google, Rambler, others), or got from more informed comrades. As a result of understanding, there should be made enumeration of inputs-outputs, their types, properties, allowed on them operations. Also, there should be found out commonalities in input-output parameters, such parameters should be grouped, new parameters, showing cardinalities of such groups should also be taken into consideration. So, not only just getting information on inputs-outputs, but operations of generalization should be applied to them. Next step is to consider possible operations application to input data in order to get output. For this purpose, it may be useful parameterization of stated problem, and trying to relate required problem with the same problems of less dimensions (characterized by less values of associated parameters). At first turn, should be considered operations, which are involved in the description of stated task. If such relation may be obtained, we get a recurrent formula, allowing getting next solution if we have previous. So, if to consider minimal possible values of parameters, and if assume that solutions of them are available, then, in the loop, will be obtained desired solution. So, we come to formulation of the set of sub queries for finding solutions of more simple problems, or made decomposition of our problem into sub problems each of which may be considered similarly unless we come to problems with known solutions. Such way of minding is character for many decision making processes, for instance, dynamic programming [5]. And such a formal approach gives opportunity of making decomposition of tasks on subtasks, which is a humans responsibility now. For example, if the task is to add 100 particular numbers, our system should get information, what are the numbers objects, what operations are applicable to them, analyze numbers, find out that all of them are of the same type, introduce parameter of the task number n of added numbers, and introduce S(x,n), where S is output, depending on group x of numbers having same type, number of which is n. If to consider closest task, S(x, n-1), characterized by slightly less value of parameter, by properties of addition operation, it may be found that S(x,n)=S(x, n-1)+x(n), where x(i) is i-th element of array x. Taking into account that S(x,1)=x(1), we get that solution of minimal required sub problem is known, and next solutions may be obtained using recurrent formula. So, system may generate code for getting solution of this problem:
S=x(1);
For i=2 to n do
S=S+x(i);
Such a system will be self-programming, all necessary codes it will be able to generate on the base of performed decomposition.
Of course, considered example is too trivial, but it illustrates main idea of the proposed approach in formalization of decision making process which may result in self-programming, so system will be able to extend its skills, by generalization of previously obtained solutions it will upgrade its level of knowledge and decrease response times for next queries.
3. Main idea of the proposal is to elaborate procedure of specifying inputs-outputs of desired problem (may be not known to the system), introducing of general parameters of the task, finding associated with it operations and their properties, making attempts of combining this information to get formula (recurrent, or not) relating solutions of the same task with less parameters values, or some other close to desired, tasks but which are slightly simpler. This leads to decomposition of initial task on simpler sub tasks, each of which may be considered similarly. If to realize such an algorithm, it may be viewed as basic for new class of computer systems capable to make their own decisions in response to requirements of its internal world (for instance, self reparation) and external world (resistance to harmful affects of viruses, environment, etc.), lead to significantly higher level of security of computer systems. Such an algorithm will be similar to basic algorithm of behavior of contemporary computers (fetch-analyze-execute infinite loop), but of significantly higher level (fetch next query - analyze it decompose/execute infinite loop) which results in creation of respective executable codes, actually responding to query. If respective executables are already ready, then they will be executed, as in conventional approach.
1. E.W.Dijkstra, Structured programming, Aug, 1969,
http://www.cs.utexas.edu/users/EWD/transcriptions/EWD02xx/EWD268.html (Nato Science Committee, 1969, Rome, pp. 93-99).
2. G.Booch, J.Rumbaugh, J.Jacobson, The Unified Modeling Language Reference Manual, Addison-Wesley, 1998, 576 p.
3. J.W.S.Liu, Real-Time Systems, Prentice Hall, Upper Saddle River, New Jersey, 2000, 610 p.
4. R.Wilson, The trouble with Rover is revealed, EE Times, Feb. 20, 2004,
http://www.eetimes.com/sys/news/OEG20040220S0046
5. M.A.Trick, A Tutorial on Dynamic Programming, Mini V, 1997,
http://mat.gsia.cmu.edu/classes/dynamic/dynamic.html
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