An expressively complete linear time temporal logic for Mazurkiewicz traces

A basic result concerning LTL, the propositional temporal logic of linear time, is that it is expressively complete; it is equal in expressive power to the first order theory of sequences. We present here a smooth extension of this result to the class of partial orders known as Mazurkiewicz traces. These partial orders arise in a variety of contexts in concurrency theory and they provide the conceptual basis for many of the partial order reduction methods that have been developed in connection with LTL-specifications. We show that LTrL, our linear time temporal logic, is equal in expressive power to the first order theory of traces when interpreted over (finite and) infinite traces. This result fills a prominent gap in the existing logical theory of infinite traces. LTrL also provides a syntactic characterisation of the so-called trace consistent (robust) LTL-specifications. These are specifications expressed as LTL formulas that do not distinguish between different linearisations of the same trace and hence are amenable to partial order reduction methods

On the mathematics of data centre network topologies.

In a recent paper, combinatorial designs were used to construct switch-centric data centre networks that compare favourably with the ubiquitous (enhanced) fat-tree data centre networks in terms of the number of servers within (given a fixed server-to-server diameter). Unfortunately there were flaws in some of the proofs in that paper. We correct these flaws here and extend the results so as to prove that the core combinatorial construction, namely the 3-step construction, results in data centre networks with optimal path diversity

On the mathematics of data centre network topologies

In a recent paper, combinatorial designs were used to construct switch-centric data centre networks that compare favourably with the ubiquitous (enhanced) fat-tree data centre networks in terms of the number of servers within (given a fixed server-to-server diameter). Unfortunately there were flaws in some of the proofs in that paper. We correct these flaws here and extend the results so as to prove that the core combinatorial construction, namely the 3-step construction, results in data centre networks with optimal path diversity

Базовый алгоритм действия системы поддержки принятия решений

We consider two-player parity games played on transition graphs of higher order pushdown automata. They are ``game-equivalent'' to a kind of model-checking game played on graphs of the infinite hierarchy introduced recently by Caucal. Then in this hierarchy we show how to reduce a game to a graph of lower level. This leads to an effective solution and a construction of the winning strategies

New results on pushdown module checking with imperfect information

Model checking of open pushdown systems (OPD) w.r.t. standard branching temporal logics (pushdown module checking or PMC) has been recently investigated in the literature, both in the context of environments with perfect and imperfect information about the system (in the last case, the environment has only a partial view of the system's control states and stack content). For standard CTL, PMC with imperfect information is known to be undecidable. If the stack content is assumed to be visible, then the problem is decidable and 2EXPTIME-complete (matching the complexity of PMC with perfect information against CTL). The decidability status of PMC with imperfect information against CTL restricted to the case where the depth of the stack content is visible is open. In this paper, we show that with this restriction, PMC with imperfect information against CTL remains undecidable. On the other hand, we individuate an interesting subclass of OPDS with visible stack content depth such that PMC with imperfect information against the existential fragment of CTL is decidable and in 2EXPTIME. Moreover, we show that the program complexity of PMC with imperfect information and visible stack content against CTL is 2EXPTIME-complete (hence, exponentially harder than the program complexity of PMC with perfect information, which is known to be EXPTIME-complete).Comment: In Proceedings GandALF 2011, arXiv:1106.081

Minimal disconnected cuts in planar graphs

The problem of finding a disconnected cut in a graph is NP-hard in general but polynomial-time solvable on planar graphs. The problem of finding a minimal disconnected cut is also NP-hard but its computational complexity is not known for planar graphs. We show that it is polynomial-time solvable on 3-connected planar graphs but NP-hard for 2-connected planar graphs. Our technique for the first result is based on a structural characterization of minimal disconnected cuts in 3-connected K 3,3 -free-minor graphs and on solving a topological minor problem in the dual. We show that the latter problem can be solved in polynomial-time even on general graphs. In addition we show that the problem of finding a minimal connected cut of size at least 3 is NP-hard for 2-connected apex graphs

Reachability for dynamic parametric processes

In a dynamic parametric process every subprocess may spawn arbitrarily many, identical child processes, that may communicate either over global variables, or over local variables that are shared with their parent. We show that reachability for dynamic parametric processes is decidable under mild assumptions. These assumptions are e.g. met if individual processes are realized by pushdown systems, or even higher-order pushdown systems. We also provide algorithms for subclasses of pushdown dynamic parametric processes, with complexity ranging between NP and DEXPTIME.Comment: 31 page

Growth and properties of ferromagnetic In(1-x)Mn(x)Sb alloys

We discuss a new narrow-gap ferromagnetic (FM) semiconductor alloy, In(1-x)Mn(x)Sb, and its growth by low-temperature molecular-beam epitaxy. The magnetic properties were investigated by direct magnetization measurements, electrical transport, magnetic circular dichroism, and the magneto-optical Kerr effect. These data clearly indicate that In(1-x)Mn(x)Sb possesses all the attributes of a system with carrier-mediated FM interactions, including well-defined hysteresis loops, a cusp in the temperature dependence of the resistivity, strong negative magnetoresistance, and a large anomalous Hall effect. The Curie temperatures in samples investigated thus far range up to 8.5 K, which are consistent with a mean-field-theory simulation of the carrier-induced ferromagnetism based on the 8-band effective band-orbital method.Comment: Invited talk at 11th International Conference on Narrow Gap Semiconductors, Buffalo, New York, U.S.A., June 16 - 20, 200