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1

Deterministic One-Way Turing Machines with Sublinear Space

Kutrib M., Provillard J., Vaszil G., Wendlandt M.

Fundamenta Informaticae

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2015

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Vol. 136, nr 1/2

139--155

EN

Deterministic one-way Turing machines with sublinear space bounds are systematically studied. We distinguish among the notions of strong, weak, and restricted space bounds. The latter is motivated by the study of P automata. The space available on the work tape depends on the number of input symbols read so far, instead of the entire input. The class of functions space constructible by such machines is investigated, and it is shown that every function f that is space constructible by a deterministic two-way Turing machine, is space constructible by a strongly f space-bounded deterministic one-way Turing machine as well. We prove that the restricted mode coincides with the strong mode for space constructible functions. The known infinite, dense, and strict hierarchy of strong space complexity classes is derived also for the weak mode by Kolmogorov complexity arguments. Finally, closure properties under AFL operations, Boolean operations and reversal are shown.

2

Catalytic and Purely Catalytic P Systems and P Automata: Control Mechanisms for Obtaining Computational Completeness

Freund R., Oswald M., Păun G.

Fundamenta Informaticae

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2015

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Vol. 136, nr 1/2

59--84

EN

The questions whether catalytic P systems with only one catalyst and purely catalytic P systems with only two catalysts can already be computationally complete in the generative case, still are open problems. For accepting P systems or P automata, the situation is even more complicated when we consider sets of vectors of natural numbers and not only sets of natural numbers – the number of catalysts increases with the dimension of the vectors. We here establish computational completeness for catalytic P systems and P automata with only one catalyst as well as for purely catalytic P systems and P automata with only two catalysts in the skin membrane by using specific variants of additional control mechanisms: in P systems and P automata with label selection, we only use rules from one set of a finite number of sets of rules in each computation step; in time-varying P systems and P automata the available sets of rules change periodically with time. The same control mechanisms also allow for computing partial recursive relations or functions of (vectors of) natural numbers when being used in catalytic P systems with one catalyst and purely catalytic P systems with two catalysts. Finally, these variants of P systems can also be used to generate or accept strings and to compute partial relations or functions on strings, and again we obtain computational completeness with only one catalyst in the case of catalytic P systems and two catalysts in the case of purely catalytic P systems.

3

Universal Query Language for Unified State Model

Wiśniewski P., Stencel K.

Fundamenta Informaticae

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2014

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Vol. 129, nr 1/2

177--192

EN

Unified State Model (USM) is a single data model that allows conveying objects of major programming languages and databases. USM exploits and emphasizes common properties of their data models. USM is equipped with mappings from these data models onto it. With USM at hand, we have faced the next natural research question whether numerous query languages for the data subsumed by USM can be clearly mapped onto a common language. We have designed and proposed such a language called the Unified Query Language (UQL). UQL is intended to be a minimalistic and elegant query language that allows expressing queries of languages of data models covered by USM. In this paper we define UQL and its concise set of operators. Next we conduct a mild introduction into UQL features by showing examples of SQL and ODMG OQL queries and their mapping onto UQL. We conclude by presenting the mapping of the theoretical foundations of these two major query languages onto UQL. They are the multiset relational algebra and the object query algebra. This is an important step towards the establishment of a fully-fledged common query language for USM and its subsumed data models.

4

Preprocessing for Network Reconstruction : Feasibility Test and Handling Infeasibility

Wagler A. K., Wegener J.-T.

Fundamenta Informaticae

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2014

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Vol. 135, nr 4

521--535

EN

The context of this work is the reconstruction of Petri net models for biological systems from experimental data. Such methods aim at generating all network alternatives fitting the given data. For a successful reconstruction, the data need to satisfy two properties: reproducibility and monotonicity. In this paper, we focus on a necessary preprocessing step for a recent reconstruction approach. We test the data for reproducibility, provide a feasibility test to detect cases where the reconstruction from the given data may fail, and provide a strategy to cope with the infeasible cases. After having performed the preprocessing step, it is guaranteed that the (given or modified) data are appropriate as input for the main reconstruction algorithm.