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Verifying and comparing finite state machines for systems that have distributed interfaces
This paper concerns state-based systems that interact with their environment at physically distributed interfaces, called ports. When such a system is used a projection of the global trace, a local trace, is observed at each port. As a result the environment has reduced observational power: the set of local traces observed need not define the global trace that occurred. We consider the previously defined implementation relation ⊆s and prove that it is undecidable whether N ⊆s M and so it is also undecidable whether testing can distinguishing two states or FSMs. We also prove that a form of model-checking is undecidable when we have distributed observations and give conditions under which N ⊆s M is decidable. We then consider implementation relation ⊆sk that concerns input sequences of length κ or less. If we place bounds on κ and the number of ports then we can decide N ⊆sk M in polynomial time but otherwise this problem is NP-hard
On Conditional Decomposability
The requirement of a language to be conditionally decomposable is imposed on
a specification language in the coordination supervisory control framework of
discrete-event systems. In this paper, we present a polynomial-time algorithm
for the verification whether a language is conditionally decomposable with
respect to given alphabets. Moreover, we also present a polynomial-time
algorithm to extend the common alphabet so that the language becomes
conditionally decomposable. A relationship of conditional decomposability to
nonblockingness of modular discrete-event systems is also discussed in this
paper in the general settings. It is shown that conditional decomposability is
a weaker condition than nonblockingness.Comment: A few minor correction
Distributed Graph Automata and Verification of Distributed Algorithms
Combining ideas from distributed algorithms and alternating automata, we
introduce a new class of finite graph automata that recognize precisely the
languages of finite graphs definable in monadic second-order logic. By
restricting transitions to be nondeterministic or deterministic, we also obtain
two strictly weaker variants of our automata for which the emptiness problem is
decidable. As an application, we suggest how suitable graph automata might be
useful in formal verification of distributed algorithms, using Floyd-Hoare
logic.Comment: 26 pages, 6 figures, includes a condensed version of the author's
Master's thesis arXiv:1404.6503. (This version of the article (v2) is
identical to the previous one (v1), except for minor changes in phrasing.
Detecting emergent processes in cellular automata with excess information
Many natural processes occur over characteristic spatial and temporal scales.
This paper presents tools for (i) flexibly and scalably coarse-graining
cellular automata and (ii) identifying which coarse-grainings express an
automaton's dynamics well, and which express its dynamics badly. We apply the
tools to investigate a range of examples in Conway's Game of Life and Hopfield
networks and demonstrate that they capture some basic intuitions about emergent
processes. Finally, we formalize the notion that a process is emergent if it is
better expressed at a coarser granularity.Comment: 8 pages, 6 figure
Intrinsically universal one-dimensional quantum cellular automata in two flavours
We give a one-dimensional quantum cellular automaton (QCA) capable of
simulating all others. By this we mean that the initial configuration and the
local transition rule of any one-dimensional QCA can be encoded within the
initial configuration of the universal QCA. Several steps of the universal QCA
will then correspond to one step of the simulated QCA. The simulation preserves
the topology in the sense that each cell of the simulated QCA is encoded as a
group of adjacent cells in the universal QCA. The encoding is linear and hence
does not carry any of the cost of the computation. We do this in two flavours:
a weak one which requires an infinite but periodic initial configuration and a
strong one which needs only a finite initial configuration. KEYWORDS: Quantum
cellular automata, Intrinsic universality, Quantum computation.Comment: 27 pages, revtex, 23 figures. V3: The results of V1-V2 are better
explained and formalized, and a novel result about intrinsic universality
with only finite initial configurations is give
Distribution of Behaviour into Parallel Communicating Subsystems
The process of decomposing a complex system into simpler subsystems has been
of interest to computer scientists over many decades, for instance, for the
field of distributed computing. In this paper, motivated by the desire to
distribute the process of active automata learning onto multiple subsystems, we
study the equivalence between a system and the total behaviour of its
decomposition which comprises subsystems with communication between them. We
show synchronously- and asynchronously-communicating decompositions that
maintain branching bisimilarity, and we prove that there is no decomposition
operator that maintains divergence-preserving branching bisimilarity over all
LTSs.Comment: In Proceedings EXPRESS/SOS 2019, arXiv:1908.0821
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