11,529 research outputs found
Synchronizing weighted automata
We introduce two generalizations of synchronizability to automata with
transitions weighted in an arbitrary semiring K=(K,+,*,0,1). (or equivalently,
to finite sets of matrices in K^nxn.) Let us call a matrix A
location-synchronizing if there exists a column in A consisting of nonzero
entries such that all the other columns of A are filled by zeros. If
additionally all the entries of this designated column are the same, we call A
synchronizing. Note that these notions coincide for stochastic matrices and
also in the Boolean semiring. A set M of matrices in K^nxn is called
(location-)synchronizing if M generates a matrix subsemigroup containing a
(location-)synchronizing matrix. The K-(location-)synchronizability problem is
the following: given a finite set M of nxn matrices with entries in K, is it
(location-)synchronizing?
Both problems are PSPACE-hard for any nontrivial semiring. We give sufficient
conditions for the semiring K when the problems are PSPACE-complete and show
several undecidability results as well, e.g. synchronizability is undecidable
if 1 has infinite order in (K,+,0) or when the free semigroup on two generators
can be embedded into (K,*,1).Comment: In Proceedings AFL 2014, arXiv:1405.527
Testing real-time systems using TINA
The paper presents a technique for model-based black-box conformance testing of real-time systems using the Time Petri Net Analyzer TINA. Such test suites are derived from a prioritized time Petri net composed of two concurrent sub-nets specifying respectively the expected behaviour of the system under test and its environment.We describe how the toolbox TINA has been extended to support automatic generation of time-optimal test suites. The result is optimal in the sense that the set of test cases in the test suite have the shortest possible accumulated time to be executed. Input/output conformance serves as the notion of implementation correctness, essentially timed trace inclusion taking environment assumptions into account. Test cases selection is based either on using manually formulated test purposes or automatically from various coverage criteria specifying structural criteria of the model to be fulfilled by the test suite. We discuss how test purposes and coverage criterion are specified in the linear temporal logic SE-LTL, derive test sequences, and assign verdicts
Physics as Quantum Information Processing: Quantum Fields as Quantum Automata
Can we reduce Quantum Field Theory (QFT) to a quantum computation? Can
physics be simulated by a quantum computer? Do we believe that a quantum field
is ultimately made of a numerable set of quantum systems that are unitarily
interacting? A positive answer to these questions corresponds to substituting
QFT with a theory of quantum cellular automata (QCA), and the present work is
examining this hypothesis. These investigations are part of a large research
program on a "quantum-digitalization" of physics, with Quantum Theory as a
special theory of information, and Physics as emergent from the same
quantum-information processing. A QCA-based QFT has tremendous potential
advantages compared to QFT, being quantum "ab-initio" and free from the
problems plaguing QFT due to the continuum hypothesis. Here I will show how
dynamics emerges from the quantum processing, how the QCA can reproduce the
Dirac-field phenomenology at large scales, and the kind of departures from QFT
that that should be expected at a Planck-scale discreteness. I will introduce
the notions of linear field quantum automaton and local-matrix quantum
automaton, in terms of which I will provide the solution to the Feynman's
problem about the possibility of simulating a Fermi field with a quantum
computer.Comment: This version: further improvements in notation. Added reference. Work
presented at the conference "Foundations of Probability and Physics-6" (FPP6)
held on 12-15 June 2011 at the Linnaeus University, Vaaxjo, Sweden. Many new
results, e.g. Feynman problem of qubit-ization of Fermi fields solved
Disjunctive bases: normal forms and model theory for modal logics
We present the concept of a disjunctive basis as a generic framework for
normal forms in modal logic based on coalgebra. Disjunctive bases were defined
in previous work on completeness for modal fixpoint logics, where they played a
central role in the proof of a generic completeness theorem for coalgebraic
mu-calculi. Believing the concept has a much wider significance, here we
investigate it more thoroughly in its own right. We show that the presence of a
disjunctive basis at the "one-step" level entails a number of good properties
for a coalgebraic mu-calculus, in particular, a simulation theorem showing that
every alternating automaton can be transformed into an equivalent
nondeterministic one. Based on this, we prove a Lyndon theorem for the full
fixpoint logic, its fixpoint-free fragment and its one-step fragment, a Uniform
Interpolation result, for both the full mu-calculus and its fixpoint-free
fragment, and a Janin-Walukiewicz-style characterization theorem for the
mu-calculus under slightly stronger assumptions.
We also raise the questions, when a disjunctive basis exists, and how
disjunctive bases are related to Moss' coalgebraic "nabla" modalities. Nabla
formulas provide disjunctive bases for many coalgebraic modal logics, but there
are cases where disjunctive bases give useful normal forms even when nabla
formulas fail to do so, our prime example being graded modal logic. We also
show that disjunctive bases are preserved by forming sums, products and
compositions of coalgebraic modal logics, providing tools for modular
construction of modal logics admitting disjunctive bases. Finally, we consider
the problem of giving a category-theoretic formulation of disjunctive bases,
and provide a partial solution
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