5,306 research outputs found
Automatic Generation of Minimal Cut Sets
A cut set is a collection of component failure modes that could lead to a
system failure. Cut Set Analysis (CSA) is applied to critical systems to
identify and rank system vulnerabilities at design time. Model checking tools
have been used to automate the generation of minimal cut sets but are generally
based on checking reachability of system failure states. This paper describes a
new approach to CSA using a Linear Temporal Logic (LTL) model checker called BT
Analyser that supports the generation of multiple counterexamples. The approach
enables a broader class of system failures to be analysed, by generalising from
failure state formulae to failure behaviours expressed in LTL. The traditional
approach to CSA using model checking requires the model or system failure to be
modified, usually by hand, to eliminate already-discovered cut sets, and the
model checker to be rerun, at each step. By contrast, the new approach works
incrementally and fully automatically, thereby removing the tedious and
error-prone manual process and resulting in significantly reduced computation
time. This in turn enables larger models to be checked. Two different
strategies for using BT Analyser for CSA are presented. There is generally no
single best strategy for model checking: their relative efficiency depends on
the model and property being analysed. Comparative results are given for the
A320 hydraulics case study in the Behavior Tree modelling language.Comment: In Proceedings ESSS 2015, arXiv:1506.0325
Generation and Properties of Snarks
For many of the unsolved problems concerning cycles and matchings in graphs
it is known that it is sufficient to prove them for \emph{snarks}, the class of
nontrivial 3-regular graphs which cannot be 3-edge coloured. In the first part
of this paper we present a new algorithm for generating all non-isomorphic
snarks of a given order. Our implementation of the new algorithm is 14 times
faster than previous programs for generating snarks, and 29 times faster for
generating weak snarks. Using this program we have generated all non-isomorphic
snarks on vertices. Previously lists up to vertices have been
published. In the second part of the paper we analyze the sets of generated
snarks with respect to a number of properties and conjectures. We find that
some of the strongest versions of the cycle double cover conjecture hold for
all snarks of these orders, as does Jaeger's Petersen colouring conjecture,
which in turn implies that Fulkerson's conjecture has no small counterexamples.
In contrast to these positive results we also find counterexamples to eight
previously published conjectures concerning cycle coverings and the general
cycle structure of cubic graphs.Comment: Submitted for publication V2: various corrections V3: Figures updated
and typos corrected. This version differs from the published one in that the
Arxiv-version has data about the automorphisms of snarks; Journal of
Combinatorial Theory. Series B. 201
Verification of Sequential Circuits by Tests-As-Proofs Paradigm
We introduce an algorithm for detection of bugs in sequential circuits. This
algorithm is incomplete i.e. its failure to find a bug breaking a property P
does not imply that P holds. The appeal of incomplete algorithms is that they
scale better than their complete counterparts. However, to make an incomplete
algorithm effective one needs to guarantee that the probability of finding a
bug is reasonably high. We try to achieve such effectiveness by employing the
Test-As-Proofs (TAP) paradigm. In our TAP based approach, a counterexample is
built as a sequence of states extracted from proofs that some local variations
of property P hold. This increases the probability that a) a representative set
of states is examined and that b) the considered states are relevant to
property P.
We describe an algorithm of test generation based on the TAP paradigm and
give preliminary experimental results
House of Graphs: a database of interesting graphs
In this note we present House of Graphs (http://hog.grinvin.org) which is a
new database of graphs. The key principle is to have a searchable database and
offer -- next to complete lists of some graph classes -- also a list of special
graphs that already turned out to be interesting and relevant in the study of
graph theoretic problems or as counterexamples to conjectures. This list can be
extended by users of the database.Comment: 8 pages; added a figur
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