Knowledge-Based Software Engineering (KBSE) is a technique, which applies expert systems to the compilation of code. These systems are also known by the term, “expert compiler” [5J. Hindin, "Intelligent tools automate high-level language programming", Comput. Des. (Winchester), vol. 25, pp. 45-56.].

Automatic programming is not new technology [6A.W. Biermann, "Automatic programming, A tutorial on formal methodologies", J. Symbolic Comp., vol. 1, no. 2, .
[http://dx.doi.org/10.1016/S0747-7171(85)80010-9] , 7E.A. Feigenbaum, and P. McCorduck, The fifth generation: Artificial intelligence and Japan’s computer challenge to the world., Addison-Wesley Pub. Co.: Reading, MA, .]. What is relatively new is the scalability of the same through the use of multiple cores and distributed server computation.

Automatic programming requires the use of some sort of specification language. This can serve as a port of entry for cyber intrusion. What is needed here are multiple specification languages, or at least compilations, to defray the effectiveness of cyberattacks. The generation of KBSE is a spiral development process. Thus, cyber protection requires domain understanding. One solution is distributed software synthesis. Here, one expert compiler calls another in a graph representation of invocation patterns. Notice that algorithmic synthesis depends upon reuse at the highest or most-abstract level. This effectively serves as a highest-level programming language with the side-benefit of providing relatively cyber-secure output codes as previously described.

It follows that the science and particularly the engineering of cyber-secure systems is a consequence of building expert compilers. Such compilers will need to create functions (i.e., functional programming) to insure interchangeability among the various functions. Global variables, other than those connected with blackboards and non-monotonic reasoning, are notoriously difficult to compile. That is the reason why the scope of synthesized code and variables need be local as a practical matter.

One way to write code, which writes code, is to build a distributed networked expert compiler, which synthesizes some space of functional programs. The code to be synthesized first are rules for synthesizing code. Here, design decisions can be generalized to provide more options for the synthesized rules. This is a form of bootstrapping for cracking the knowledge acquisition bottleneck [7E.A. Feigenbaum, and P. McCorduck, The fifth generation: Artificial intelligence and Japan’s computer challenge to the world., Addison-Wesley Pub. Co.: Reading, MA, .].

The way to write meta-rules is to group rules into segments, which are applied by other rules [8S. Minton, Learning search control knowledge: An explanation based approach., Kluwer International Series in Engineering and Computer Science: New York, p. 61.
[http://dx.doi.org/10.1007/978-1-4613-1703-6] ]. Segments are cohesive; and, as a consequence, rules and groups of rules can be grouped by chance on the basis of synthesizing code, which functions in satisfaction of sets of I/O constraints. While the validation of arbitrary code can be achieved by expert systems of arbitrary complexity, functional code is amenable to I/O testing by making use of orthogonal sets of I/O pairs. A pair of I/O pairs is said to be orthogonal with respect to a software function if the two I/O tests do not share the same execution path trace. In practice, such pairings of I/O tests need only be relatively orthogonal as a cost-saving measure. For example, an orthogonal set of sort program tests is {((3 2 1) (1 2 3)) ((3 1 2) (1 2 3)) ((1 2 3) (1 2 3))}. A pair of non-orthogonal tests is, for example, {((2 1) (1 2)) ((3 2 1) (1 2 3))}. The key to identifying relatively orthogonal test vectors is that the set of them is random in the recursively enumerable sense [9G.J. Chaitin, "Randomness and mathematical proof", Sci. Am., vol. 232, no. 5, pp. 47-52.
[http://dx.doi.org/10.1038/scientificamerican0575-47] ]. That is, the test vectors should not be functionally related to each other. Validated functions can be further composed and similarly tested for novel functionality.

So far, we have seen that the problem of providing practical cybersecurity is tied to the problem of automatic programming. This problem, in turn, is tied to the problem of knowledge acquisition.

Knowledge acquisition goes beyond neural networks. Indeed, effective knowledge acquisition by humans involves transformational analogy, which is something that neural networks cannot do [10H. Hosseini, and R. Poovendran, Deep neural networks do not recognize negative images, work was supported by ONR grants N00014-14-1-0029 and N00014-16-1-2710, ARO grant W911NF-16-1-0485, and NSF grant CNS-1446866, pp. 1-3, 2017., 11H. Hosseini, Deceiving google’s perspective API built for detecting toxic comments, work was supported by ONR grants N00014-14-1-0029 and N00014-16-1-2710 and ARO grant W911NF-16-1-0485, pp. 1-4, 2017.]. This then is the domain for symbolic AI, since neural networks inherently cannot perform basic “modus ponens”.

The key to successful KBSE is having as much knowledge in as many representational formalisms [12S. Amarel, "On representations of problems of reasoning about actions", Math. Intell., vol. 3, pp. 131-171.] as possible available to bear. In theory, one needs as high a density of knowledge as possible, which cannot be bounded [13S.H. Rubin, "On randomization and discovery", Inf. Sci., vol. 177, no. 1, pp. 170-191.
[http://dx.doi.org/10.1016/j.ins.2006.06.001] ].

It is acknowledged that there is a software, which cannot be sufficiently characterized by a non-deterministic stochastic I/O mapping. For example, a component might draw a picture. Here, a knowledge-based and/or neural system may be applied to rank the quality of the component. In a sense, mapping input to desired output(s) is universal, it’s just that intermediate evaluation code is sometimes needed. Thus, while we will not address such complexities in this paper, it is to be understood that the methodology advanced herein is completely compatible with them. In fact, it may be used to define the intermediate knowledge-based evaluation systems.

Another point of contention pertains to the use of empirical testing instead of, or in combination with, denotational or axiomatic semantics for program validation. The recursive Unsolvability of the Equivalence Problem [1A.J. Kfoury, R.N. Moll, and M.A. Arbib, A Programming approach to computability., Springer-Verlag Inc.: New York, NY, .
[http://dx.doi.org/10.1007/978-1-4612-5749-3] ] proves that in the general case it is impossible to prove that two arbitrary programs compute the same function. Moreover, approaches to program validation, based on computational semantics, have proven to be unacceptably difficult to apply in practice. There can be no theoretical method for insuring absolute validity once a program grows to a level of complexity to be capable of self-reference [1A.J. Kfoury, R.N. Moll, and M.A. Arbib, A Programming approach to computability., Springer-Verlag Inc.: New York, NY, .
[http://dx.doi.org/10.1007/978-1-4612-5749-3] , 13S.H. Rubin, "On randomization and discovery", Inf. Sci., vol. 177, no. 1, pp. 170-191.
[http://dx.doi.org/10.1016/j.ins.2006.06.001] , 16M.A. Arbib, A.J. Kfoury, and R.N. Moll, A basis for theoretical computer science., Springer-Verlag: New York, NY, .
[http://dx.doi.org/10.1007/978-1-4613-9455-6] , 17V.A. Uspenskii, Gödel’s incompleteness theorem, translated from Russian., Ves Mir Publishers: Moscow, .].

It follows that program validation is properly based on empirical testing, the goal of which is to cover a maximal number of execution paths using a minimal number of test cases. This is none other than randomization [9G.J. Chaitin, "Randomness and mathematical proof", Sci. Am., vol. 232, no. 5, pp. 47-52.
[http://dx.doi.org/10.1038/scientificamerican0575-47] , 13S.H. Rubin, "On randomization and discovery", Inf. Sci., vol. 177, no. 1, pp. 170-191.
[http://dx.doi.org/10.1016/j.ins.2006.06.001] ]. Of course, there is no need to achieve the absolute minimum here; a minimum relative to the search time required to find the test cases will suffice. In a large enough system of systems, the methodology advanced herein may be applied to the generation of relatively random test cases. Randomization serves to maximize reuse. Reuse is perhaps the best real-world technique for exposing and thus minimizing the occurrence of program bugs.

Each component, saved in the database, is associated with one or more I/O test vector pairings that serve to map a random input vector to correct non deterministic output vectors. The underpinning principle is that test vectors, which have been sufficiently randomized, are relatively incompressible. For example, consider the synthesis of a sort function using LISP (Fig. 2). There are some extraneous details, such as knowing when a particular sequence will lead to a stack overflow; but, these are easily resolved using an allowed execution time parameter. Impressive programs have been so synthesized; supporting the component-based concept. Notice that components can be written at any scale from primitive statements to complex functions. Given only so much allocated search time, the system will either discover a solution or report back with failure. This is in keeping with the recursive Unsolvability of the Halting Problem [1A.J. Kfoury, R.N. Moll, and M.A. Arbib, A Programming approach to computability., Springer-Verlag Inc.: New York, NY, .
[http://dx.doi.org/10.1007/978-1-4612-5749-3] , 13S.H. Rubin, "On randomization and discovery", Inf. Sci., vol. 177, no. 1, pp. 170-191.
[http://dx.doi.org/10.1016/j.ins.2006.06.001] ].

Fig. (2) Function synthesis using random-basis testing.

Consider such I/O constraints as (((3 2 1) (1 2 3)) ((3 1 2) (1 2 3))). That is, when (3 2 1) is input to the sort function, it is required to output (1 2 3). Similarly, when (3 1 2) is input to it, it is required to output the same. Clearly, there is little value in using a test set such as (((1) (1)) ((2 1) (1 2)) ((3 2 1) (1 2 3)) ((4 3 2 1) (1 2 3 4)) …).

The purpose served by case I/O exemplar vectors, such as illustrated above, is to filter out synthesized functions, which do not satisfy the specified mapping constraints. A super set of such functions can thus be filtered down to a non-deterministic set of functions. The I/O test vectors must be mutually random so as to maximize the number of distinct execution paths tested. This helps to insure that the selected function(s) will perform, as desired, on unspecified input vectors. Moreover, in as much as every function is synthesized as a random instance of its parent schema, semantically equivalent non-deterministic functions are likely to be syntactically distinct. Almost certainly, they will be syntactically distinct in the context of other synthesized and composed functions. This is sufficient to insure cyber security.

One problem, which occurs in the synthesis of large complex functions is that the candidate instantiation space is too large to permit tractable testing. One solution to this problem follows from the inverse triangle inequality. This means that one can effect an exponential reduction in the search space for functional instances by moving the articulation points into distinct functions, which can always be done. This moves the increase in complexity for the moved articulation point from the product of possible instances for that articulation point to the sum of possible instances for that articulation point. When this is carried out for several articulation points, in the same function, the cumulative savings in the size of the search space is clearly exponential. Moreover, the search space for function synthesis can be further reduced by independently synthesizing each function in a composition of functions and then separately validating the composition. Another technique for saving time is to evaluate each salient set of I/O constraints to the point of failure, if any. Just as is the case with “or” and “and” functions, there is no need to evaluate past the point of failure. Given that the vast majority of synthesized functions will be failures, this one strategy can collectively save considerable time. Another very-important approach to delimiting search is to employ search control heuristics. For example, in Pascal, every end keyword needs to be preceded by an unmatched begin keyword. This knowledge, and knowledge like it, can be applied to delimit the members of the matching set articulation point. Search control heuristics enable the scaling of the methodology. This is a key concept. It should be noted how semantic randomization depends, in no small part, on knowledge insertion (i.e., unlike syntactic randomization). As Francis Bacon once stated, “knowledge is power”; in this case, power to thwart otherwise successful cyber-attacks.

A problem is that the test set is relatively symmetric or compressible into a compact generating function. A fixed-point or random test set is required instead and the use of such relatively random test sets is called, random-basis testing [18Q. Liang, and S.H. Rubin, "Randomization for testing systems of systems", Proc. 10^th IEEE Intern. Conf., Info. Reuse & Integration: Las Vegas, NV, 10-12 Aug., pp. 110-114.
[http://dx.doi.org/10.1109/IRI.2009.5211597] ]. While the need for functional decomposition remains, under random-basis testing, the complexity for the designer is shifted from writing code to writing search schema and relatively random tests. For example, such a test set here is (((1) (1)) ((2 1) (1 2)) ((3 1 2) (1 2 3)) ((1 2 3) (1 2 3))). Many similar ones exist. One may also want to constrain the complexity of any synthesized component (e.g., Insertion Sort, Quicksort, et al.). This can be accomplished through the inclusion of temporal constraints on the I/O behavior (i.e., relative to the executing hardware and competing software components) [19A.N. Kolmogorov, and V.A. Uspenskii, "On the definition of an algorithm", Russian, English Translation: Amer. Math. Soc. Translation, vol. 29 , no. 2, pp. 217-245.
[http://dx.doi.org/10.1090/trans2/029/07] ].

There are two categories of components; Boolean components, which return True or False and procedural components, which compute all other functions and can post and/or retract information to/from a blackboard. There are two blackboards; a local blackboard, which is only accessible to local component functions and procedures as well as those invoked by them and a global blackboard, which is accessible to all component functions and procedures. The blackboards dynamically augment the input vectors to provide further context.

All components are composed of rules, each of which consists of one or a conjunction of two or more Boolean components, which imply one or a sequence of two or more, procedural components; including global and local RETRACT and POST. Given an input vector and corresponding output vector(s), the rule base comprising the component must map the former to that latter at least tolerance percent of the time. The default tolerance is 100 percent. Transformation may also favor the fastest component on the same I/O characterization. Notice that greater diversification comes at an allowance for less optimization.

Cyberattacks are likely to affect one LISP construct (e.g., null S) and not another (e.g., nil) or vice versa. Given the plethora of such constructs, which comprise a typical function, some versions of syntax will remain unscathed by a cyberattack, while others will not. This is always detectable; and, processing can be rewound and continued. It follows that automatic programming enables cybersecurity; and, cybersecurity serves to advance automatic programming. It seems as though nature has provided us with a constructive consequence supporting the plethora of cyberattacks! That is, they serve to advance technologies for automatic programming, which is applied to ameliorate the cybersecurity problem.

A library of universal primitive and macro components is supplied and evolved. There are three ways that these are retrieved. First, is by name. Second is by mapping an input vector closer, by some definition (e.g., the 2-norm et al.), to a desired non deterministic output vector (i.e., hill climbing - non contracting transformations reducing the distance to a goal state with each substitution). Third is just by mapping the input vector using contracting and non-contracting transformations (i.e., Type 0 transformation). Hill climbing and Type 0 transformation may be combined and occur simultaneously until interrupted. The former accelerates reaching a desired output state, while the latter gets the system off of non-global hills.

Macro components are evolved by chance. They comprise a Very High Level Language (VHLL). For example, a macro component for predicting what crops to sow will no doubt invoke a macro component for predicting the weather. Similarly, a macro component for planning a vacation will likewise invoke the same macro component for predicting the weather (i.e., reuse) [20T. Bouabana-Tebibel, S.H. Rubin, Eds., Integration of reusable systems., Springer International Publishing: Switzerland, .
[http://dx.doi.org/10.1007/978-3-319-04717-1] ].

Test vectors are stored with each indexed component to facilitate the programmer in their creation and diversification as well as with the overall understanding of the components function. While increasing the number of software tests is generally important, a domain-specific goal is to generate mutually random ordered pairs [18Q. Liang, and S.H. Rubin, "Randomization for testing systems of systems", Proc. 10^th IEEE Intern. Conf., Info. Reuse & Integration: Las Vegas, NV, 10-12 Aug., pp. 110-114.
[http://dx.doi.org/10.1109/IRI.2009.5211597] ]. Components in satisfaction of their I/O test vectors are valid by definition. Non deterministic outputs are not stochastically defined for testing as it would be difficult to know these numbers as well as inefficient to run such quantitative tests.

As software gets more complex, one might logically expect the number of components to grow with it. Actually, the exact opposite is true. Engineers are required to obtain tighter integration among components in an effort to address cost, reliability, and packaging considerations, so they are constantly working to decrease the number of software components but deliver an ever-expanding range of capabilities. Thus, macro components have great utility. Such randomizations have an attendant advantage in that their use; including that of their constituent components implies their increased testing by virtue of their falling on a greater number of execution paths [9G.J. Chaitin, "Randomness and mathematical proof", Sci. Am., vol. 232, no. 5, pp. 47-52.
[http://dx.doi.org/10.1038/scientificamerican0575-47] , 13S.H. Rubin, "On randomization and discovery", Inf. Sci., vol. 177, no. 1, pp. 170-191.
[http://dx.doi.org/10.1016/j.ins.2006.06.001] , 19A.N. Kolmogorov, and V.A. Uspenskii, "On the definition of an algorithm", Russian, English Translation: Amer. Math. Soc. Translation, vol. 29 , no. 2, pp. 217-245.
[http://dx.doi.org/10.1090/trans2/029/07] ]. The goal here is to cover the maximum number of execution paths using the relatively fewest I/O tests (i.e., random-basis testing [18Q. Liang, and S.H. Rubin, "Randomization for testing systems of systems", Proc. 10^th IEEE Intern. Conf., Info. Reuse & Integration: Las Vegas, NV, 10-12 Aug., pp. 110-114.
[http://dx.doi.org/10.1109/IRI.2009.5211597] ]).

The maximum number of components, in a rule, as well as the maximum number of rules in a component, is determined based on the speed, number of parallel processors for any fixed hardware capability, and the complexity of processing the I/O vectors. It is assumed that macro components will make use of parallel/distributed processors to avoid a significant slowdown. Components that are not hierarchical are quite amenable to parallel synthesis and testing.

Components may not recursively (e.g., in a daisy chain) invoke themselves. This is checked at definition time through the use of an acyclic stack of generated calls. Searches for component maps are ordered from primitive components to a maximal depth of composition, which is defined in the I/O library. This is performed to maximize speed of discovery. The components satisfying the supplied mapping characterizations are recursively enumerable.

Software engineers can supply external knowledge, which is captured for the specification of components. Components are defined using a generalized language based on disjunction. This is because it is easier to specify alternatives (i.e., schemas) in satisfaction of I/O constraints than to specify single instances (e.g., A|B → C than A → C | B → C; or, A → B|C than A → B | A → C). Moreover, such an approach facilitates the automatic re-programming of component definitions in response to the use of similar I/O constraints. The idea is to let the CPU assume more of the selection task by running a specified number of rule alternates against the specified I/O constraints. This off-loads the mundane work to the machine and frees the software engineer in proportion to the processing speed of the machine. Here, the software engineer is freed to work at the conceptual level; while, the machine is enabled to work at the detailed level. Each is liberated to do what it does best. The number of (macro) Boolean components, (macro) procedural components, and alternate candidate rules is determined by the ply of each and the processing speed of the machine. Notice that the task of programming component rules is thus proportionately relaxed. Programming is not necessarily eliminated; rather, it is moved to ever-higher levels. This is randomization [9G.J. Chaitin, "Randomness and mathematical proof", Sci. Am., vol. 232, no. 5, pp. 47-52.
[http://dx.doi.org/10.1038/scientificamerican0575-47] ]. Furthermore, component-type rule-based languages have the advantage of being self-documenting (e.g., IF “Root-Problem” THEN “Newton-Iterative-Method”). Novel and efficient development environments can be designed to support the pragmatics of such programming.

Each run may synthesize semantically equivalent (i.e., within the limits defined by the I/O test vectors), but syntactically distinct functions (e.g., see the alternative definitions for MYSORT at the bottom of Fig. 2). Similar diversified components are captured in transformation rules. Thus, initially diversified components are synthesized entirely by chance, which of course can be very slow. Chance synthesis is a continual on-going process, which is necessary to maintain genetic diversity. But, once transformation rules are synthesized, they are applied to constituent component rules to create diversified components with great rapidity. The 3-2-1 skew may be applied to favor the use of recently acquired or fired transformation rules. It uses a logical move-to-the-head ordered search based upon temporal locality [21H.M. Deitel, An introduction to operating systems., Prentice Hall, Inc.: Upper Saddle River, NJ, .]. The acquisition of new components leads to the acquisition of new transforms. Note that if the system sits idle for long, it enters dream mode via the 3-2-1 skew. That is, it progressively incorporates less recently acquired/fired transforms in the search for diversified components.

Transformation rules can be set to minimize space and/or maximize speed and in so doing generalize/optimize. Such optimizations are also in keeping with Occam’s razor, which states that in selecting among competing explanations of apparent equal validity, the simplest is to be preferred. If, after each such transformation, the progressively outer components do not properly map their I/O characterization vectors, then it can only be because the pair of components comprising the transformation rule is not semantically equivalent. In this case, the transformation is undone and the transformation rule and its substituted component are expunged (i.e., since it has an unknown deleterious I/O behavior). This allows for a proper version to be subsequently re-synthesized. Components having more-specific redundant rules have those rules expunged.

Convergence upon correct components and thus correct transforms is assured. This is superior to just using multiple analogies as it provides practical (i.e., to the limits of the supplied test vectors) absolute verification at potentially multiple component levels. Such validation is not in contradiction with the Incompleteness Theorem as the test vectors are always finite as is the allowed runtime [17V.A. Uspenskii, Gödel’s incompleteness theorem, translated from Russian., Ves Mir Publishers: Moscow, .].

Non monotonic rules are secondary rules, which condition the firing of primary rules. They have the advantage of being highly reusable; facilitating the specification of complex components. Reuse is a tenet of randomization theory [13S.H. Rubin, "On randomization and discovery", Inf. Sci., vol. 177, no. 1, pp. 170-191.
[http://dx.doi.org/10.1016/j.ins.2006.06.001] ]. Both local and global blackboards utilize posting and retraction protocols. The scope of a local blackboard is limited to the originating component and all components invoked by it. For example,

{Laces: Pull untied laces, Tie: Make bow} → GRETRACT: (Foot-ware: Shoes are untied); GPOST: (Foot-ware: Shoes are tied)

The order of the predefined, global and local RETRACT and POST procedures is, akin to all procedural sequences, immutable.

The pattern-matching search known as backtracking can iteratively expand the leftmost node, or the rightmost node on Open [22N.J. Nilsson, Principles of artificial intelligence., Tioga Pub. Co.: Palo Alto, CA, .]. Results here are not identical, but are statistically equivalent. If one component is provided with one expansion search parameter, the other component must be provided with the same search parameter, or the resultant dual-component search will have some breadth-first, rather than strictly depth-first characteristics. This will change the semantics resulting from the use of large search spaces. Clearly, components need to be transformed with due regard for subtle context to preserve their aggregate semantics. These semantic differences become apparent on input vectors, which are outside of those used for I/O definition. Their use can result in erroneous communications via the local and/or global blackboards. The system of systems, described in the technical approach below, evolves such context-sensitive components and their transformations.

NNCSs can potentially provide exponentially more security than can a multi-compiler by finding multiple paths from start to goal states [2S. Singh, and S. Silakari, "A survey of cyber attack detection systems", Int. J. of Computer Science and Network Security, vol. 9, no. 5, pp. 1-10. [IJCSNS]., 22N.J. Nilsson, Principles of artificial intelligence., Tioga Pub. Co.: Palo Alto, CA, .]. Under syntactic differentiation, achieving the same results implies computing the same component semantics. Under transformational equivalence, one need not compute the same exact component semantics; only ones that achieve the same results in the context of other components. Given sufficiently large problem spaces and sufficient computational power, exponential increases in cyber security can thus be had. Syntactic differentiation can at best provide only linear increases in cybersecurity. Thus, our methodology offers far greater security against cyberattacks than can conventional approaches [3A. Gherbi, R. Charpentier, and M. Couture, "Software diversity for future systems security", Workshop on Hot Topics in Operating Systems, pp. 10pp. 57-13-72.].

The transformational process converges on the synthesis of syntactically distinct components, which are, to the limits of testing, semantically equivalent. Such components can be verified to be free from attack if their I/O synthesis behavior is within the specified tolerance. Even so, multiple “semantically equivalent” components may compute different output vectors on the same, previously untested input vectors. Here, diversity enables the use of multiple functional analogies by counting the number of diverse components yielding the same output vector. It also allows for a count of the approximate number of recursively enumerable distinct paths leading to the synthesis of each component. This multiple analogies of derivation, when combined with multiple functional analogies, provide a relative validity metric for voting the novel output vectors. These solution vectors are very important because they evidence the system capability for learning to properly generalize by way of exploiting redundancy (i.e., in both function and derivation). Furthermore, having multiple derivations provides stochastic non deterministic probabilities. This lies at the root of human imagination and knowledge.