5. Flow-processing APS

Described approach to the procedural connection makes easy integration of the distributed hardware components, linked by the computer network, into a single system with the single operation process. This may be done by procedural connection of the corresponding hardware drivers and implementation of the socalled flow-processing augmented Post systems.

FAPS KB includes along with S- and P-productions also the so-called flow (F-) productions having the form of

$$<\varsigma\_0 \to \varsigma\_1, \dots, \varsigma\_m, \varsigma\_{m+1}, d > \tag{23}$$

where terms s0, called activator, and smþ1, called actor, contain only complete variables and symbol "!" (inverse to " ", used in S-production) divides activator and body, including, along with actor, conditions s1, …, sm. This structure is rather usual as well as operational semantics of F-productions, which is defined by function F, similar to Q and RB, and interconnected with them into integrated algorithmics.

We assume that F-productions are represented in the knowledge base as couples , s0, φ, s, d . , where s<sup>0</sup> is activator, φ is set of terms-conditions, and s is actor, while d is variable declaration. By this, APS KB contains three types of objects, corresponding to three types of productions:


All these objects are accumulated to set S, which, along with metadatabase D, present in the bodies of functions Q, RB, and F as global variable.

Function F is as follows:

```
1 F : functionð Þ w ;
```

```
2 variables s0; s
                0 ð Þ term; d; δ; δ0 ð Þ ð Þ declaration; w word; φ set of terms local;
```

```
3 variablesð Þ S set of productions; D set of context�free rules global;
```

```
4 do , s0, φ, s, d . ∈S;
```

```
5 δ≔d0 s0
         w, f g ∅
         ;
```

```
6 if δ 6¼ ∇
```

```
7 then doδ0 ∈RBð Þ φ; δ ;
```
;

$$\mathbf{8} \qquad \qquad \qquad \qquad F(s[\delta']); \mathbf{8}$$

```
9 endδ0
```

```
10 endS;
```
11 terminate;

```
12 endF
```
As seen, the search on F-productions set (lines 4–10) provides selection of such F-productions, which are activated by input message w. The set of conditions of

every activated F-production is interpreted as residual body of S-production (lines 7–9). Every variable declaration δ<sup>0</sup> , obtained as a result of this interpretation, is used for the creation of new message by substitution of δ<sup>0</sup> to actor s. This message is used as input value for function F recursive application. So the wave of messages, triggered by initial message, is generated, modeling well-known blackboard architecture. This wave propagation of any programs (including DBMS, software/hardware drivers, providing activation and operation of various devices, as well as networking middleware) may be applied. Operator terminate (line 11) stops F execution, so no return to the parent call is performed.

Various practice-oriented dialects of APS, providing various effective technologies of non-procedural programming (multiactivating, triggers, terms with negators, decision tables, etc.), were developed; also described operational semantics of APS and its extensions were redefined for highly parallel hardware environment [1, 2]. Taking into account nondeterministic nature of operational semantics of APS family, some additional tools for logical inference control were introduced in [1, 2].

Let us consider now the main features of APS application to the most advanced areas—Big Data, Internet of Things, cyberphysical industry, and cybersecurity forming the future digital economy information infrastructure (DEII) [13, 14]. In all aforementioned applications, APS knowledge representation plays interconnecting and flexifying role, providing fast integration of various heterogeneous systems and fast adaptation of their operation logic to the highly volatile environment. In fact, APS simplify to the maximally possible level the most complicated problem of interoperability of any a priori developed systems; APS KB is nothing but "glue," which in the simplest regular way integrates them together.
