Reachability in Higher-Order-Counters

Higher-order counter automata (\HOCS) can be either seen as a restriction of higher-order pushdown automata (\HOPS) to a unary stack alphabet, or as an extension of counter automata to higher levels. We distinguish two principal kinds of \HOCS: those that can test whether the topmost counter value is zero and those which cannot. We show that control-state reachability for level $k$ \HOCS with $0$-test is complete for \mbox{$(k-2)$}-fold exponential space; leaving out the $0$-test leads to completeness for \mbox{$(k-2)$}-fold exponential time. Restricting \HOCS (without $0$-test) to level $2$, we prove that global (forward or backward) reachability analysis is \PTIME-complete. This enhances the known result for pushdown systems which are subsumed by level $2$ \HOCS without $0$-test. We transfer our results to the formal language setting. Assuming that \PTIME \subsetneq \PSPACE \subsetneq \mathbf{EXPTIME}, we apply proof ideas of Engelfriet and conclude that the hierarchies of languages of \HOPS and of \HOCS form strictly interleaving hierarchies. Interestingly, Engelfriet's constructions also allow to conclude immediately that the hierarchy of collapsible pushdown languages is strict level-by-level due to the existing complexity results for reachability on collapsible pushdown graphs. This answers an open question independently asked by Parys and by Kobayashi.Comment: Version with Full Proofs of a paper that appears at MFCS 201

Radiation tolerance investigation of a Si detectors and microelectronics using NSC KIPT linacs

A possibility of full irradiation tests of semiconductor detectors and microelectronics using electron accelerators are considered in the present work. The techniques for irradiation and for detector tests were described. The data on the efficiency of electron and bremsstrahlung action on the Si bulk material are presented

Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems

Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure. These systems may be used to model higher-order programs and are closely related to the Caucal hierarchy of infinite graphs and safe higher-order recursion schemes. We consider the backwards-reachability problem over higher-order Alternating PDSs (APDSs), a generalisation of higher-order PDSs. This builds on and extends previous work on pushdown systems and context-free higher-order processes in a non-trivial manner. In particular, we show that the set of configurations from which a regular set of higher-order APDS configurations is reachable is regular and computable in n-EXPTIME. In fact, the problem is n-EXPTIME-complete. We show that this work has several applications in the verification of higher-order PDSs, such as linear-time model-checking, alternation-free mu-calculus model-checking and the computation of winning regions of reachability games

Analyzing and Modeling Real-World Phenomena with Complex Networks: A Survey of Applications

The success of new scientific areas can be assessed by their potential for contributing to new theoretical approaches and in applications to real-world problems. Complex networks have fared extremely well in both of these aspects, with their sound theoretical basis developed over the years and with a variety of applications. In this survey, we analyze the applications of complex networks to real-world problems and data, with emphasis in representation, analysis and modeling, after an introduction to the main concepts and models. A diversity of phenomena are surveyed, which may be classified into no less than 22 areas, providing a clear indication of the impact of the field of complex networks.Comment: 103 pages, 3 figures and 7 tables. A working manuscript, suggestions are welcome

Idempotent mathematics and interval analysis

Idempotent mathematics, which is based on the so-called idempotent superposition principle, has achieved a significant role lately in applications to problems of optimization (optimization of graphs, discrete optimization with a large parameter, optimal organization of parallel computation, etc.). However, in practice one often deals with uncertain data so that the use of interval arithmetic (which transfers the operations with numbers to operations with sets) facilitates the work with unreliable data and the control of rounding error through the process of computation. For these reasons the authors of this extensive paper develop an analogue of interval analysis in the context of optimization theory and idempotent mathematics, that is, a generalization of idempotent mathematics for the case of operations with sets. Different kinds of interval extensions of idempotent semi-rings (the weak interval extension, interval extension with a zero element) and their properties are discussed. par It is shown that idempotent interval arithmetic has much better behavior compared to classical situation, such as the distributivity property, associativity of matrix multiplication and a polynomial number of operations in solving interval systems of linear equations. This makes this structure suitable for applications in linear algebra and even further. Namely, idempotent linear algebra lies in the essence of idempotent analysis since by the principle of superposition many nonlinear algorithms can be suitably approximated by linear algorithms. Such applications are also considered in the paper