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EN
As mine planning is one of the most complicated steps, which depends on a lot of factors as geology, economy etc., consequently, the decision-making process is difficult, due to the existence of a lot of factors for choosing the optimal mining system. In this paper, the method and the result of Analytical Hierarchical Process is presented, shown on a case study – Open pit Drmno, as one of the largest lignite mines in Serbia. The analysis included 6 criteria and two alternatives were applied as Variant 1 and Variant 2. The results show that the suitable mining system for this case study – open pit Drmno is Variant 2.
2
Content available remote Highly Undecidable Problems about Recognizability by Tiling Systems
EN
Altenbernd, Thomas and Wöhrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with usual acceptance conditions, such as the Büchi and Muller ones, in [1]. It was proved in [9] that it is undecidable whether a Büchirecognizable language of infinite pictures is E-recognizable (respectively, A-recognizable). We show here that these two decision problems are actually Π1/2/ -complete, hence located at the second level of the analytical hierarchy, and "highly undecidable". We give the exact degree of numerous other undecidable problems for Büchi-recognizable languages of infinite pictures. In particular, the nonemptiness and the infiniteness problems are Σ1/1/ -complete, and the universality problem, the inclusion problem, the equivalence problem, the determinizability problem, the complementability problem, are all Π1/2/ -complete. It is also Π1/2/ -complete to determine whether a given Büchi recognizable language of infinite pictures can be accepted row by row using an automaton model over ordinal words of length ω2/.
3
Content available remote Classes of Timed Automata and the Undecidability of Universality
EN
Universality for deterministic Timed Büchi Automata (TBA) is PSPACE-complete but becomes highly undecidable when unrestricted nondeterminism is allowed. More precisely, universality for nondeterministic TBA is P11-hard and its precise position in the analytical hierarchy is still an open question. In this paper we introduce two types of syntactical restrictions to nondeterministic TBA, which are of independent interest, and show that their universality problem is P11-complete. These restrictions define, as we prove, proper subclasses of the class of timed languages defined by nondeterministic TBA. This suggests, as we argue, that no solution to that open question will come without surprise. We also establish closure properties and the relationships between the classes of languages we describe.
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