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## Relational and Algebraic Methods in Computer Science - 19th International Conference, RAMiCS 2021, Marseille, France, November 2-5, 2021, Proceedings

We prove that, similarly to known PSPACEPSPACE-completeness of recognising 𝖥𝖮(<)FO(<)-definability of the language 𝐿(𝔄)L(A) of a DFA 𝔄A, deciding both 𝖥𝖮(<,≡)FO(<,≡)- and 𝖥𝖮(<,𝖬𝖮𝖣)FO(<,MOD)-definability (corresponding to circuit complexity in AC0AC0 and ACC0ACC0) are PSPACEPSPACE-complete. We obtain these results by first showing that known algebraic characterisations of FO-definability of 𝐿(𝔄)L(A)can be captured by ‘localisable’ properties of the transition monoid of 𝔄A. Using our criterion, we then generalise the known proof of PSPACEPSPACE-hardness of 𝖥𝖮(<)FO(<)-definability, and establish the upper bounds not only for arbitrary DFAs but also for 2NFAs.

We discuss an example of recursively-enumerable Kripke-complete first-order modal logics that are not Kripke complete with respect to a first-order definable class of frames.

We propose an automata model of computer system security. A system is represented by a finite automaton with states partitioned into two subsets: "secure" and "insecure". System functioning is secure if the number of consecutive insecure states is not greater than some nonnegative integer k. This definition allows one to formally reflect responsiveness to security breaches. The set of all input sequences that preserve security for the given value of k is referred to as a k-secure language. We prove that if a language is k-secure for some natural k and automaton V, then it is also k'-secure for any 0 <= k' <= k and some automaton V' = V' (k'). Reduction of the value of k is performed at the cost of amplification of the number of states. On the other hand, for any non-negative integer k there exists a k-secure language that is not k"-secure for any natural k" > k. The problem of reconstruction of a k-secure language using a conditional experiment is split into two subcases. If the cardinality of an input alphabet is bound by some constant, then the order of Shannon function of experiment complexity is the same for al k; otherwise there emerges a lower bound of the order n^k.

*It is common to use the first-order language as a formal tool for describing properties of various (computational) structures. On the one hand, this language is well understood and easy to use; on the other, many questions that are im-portant from the applications point of view related to this language are algorithmically undecidable, i.e., cannot be answered using a computer program. These days, there exist various alternative languages that can be used for describing computational processes and their properties, for which the corresponding questions are, in contrast to the first-order language, algorithmically decidable. In this paper, we consider one of such languages, – the language of the Computational Tree Logic (CTL). It is commonly used for program verification as it is capable of describing properties of computational processes, – in particular, properties of the binary relation used in the Kripke semantics. The authors investigate the possibility of finding algorithmically first-order formulas defining the same classes of Kripke frames as the formulas of the language of CTL. It is well known the problem of finding first-order correspondents of propositional intuitionistic formulas is algorithmically undecidable. The authors reduce – using the Gödel translation of intuitionistic formulas into modal ones, and subsequently a translation of resultant modal formulas into CTL-formulas – the first-order correspondence problem for propositional intuitionistic formulas to the first-order correspondence problem for CTL-formulas on Kripke frames. As a result of this reduction, they prove that the first-order correspondence problem for CTL-formulas is algorithmically undecidable. In the conclusion, the authors discuss some possible modifications of their construction for fragments of the language of CTL as well as algorithmic decidability of the CTL correspondence problem for first-order formulas.*

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.