3,037 research outputs found
Structural Analysis of Boolean Equation Systems
We analyse the problem of solving Boolean equation systems through the use of
structure graphs. The latter are obtained through an elegant set of
Plotkin-style deduction rules. Our main contribution is that we show that
equation systems with bisimilar structure graphs have the same solution. We
show that our work conservatively extends earlier work, conducted by Keiren and
Willemse, in which dependency graphs were used to analyse a subclass of Boolean
equation systems, viz., equation systems in standard recursive form. We
illustrate our approach by a small example, demonstrating the effect of
simplifying an equation system through minimisation of its structure graph
The complexity of Boolean surjective general-valued CSPs
Valued constraint satisfaction problems (VCSPs) are discrete optimisation
problems with a -valued objective function given as
a sum of fixed-arity functions. In Boolean surjective VCSPs, variables take on
labels from and an optimal assignment is required to use both
labels from . Examples include the classical global Min-Cut problem in
graphs and the Minimum Distance problem studied in coding theory.
We establish a dichotomy theorem and thus give a complete complexity
classification of Boolean surjective VCSPs with respect to exact solvability.
Our work generalises the dichotomy for -valued constraint
languages (corresponding to surjective decision CSPs) obtained by Creignou and
H\'ebrard. For the maximisation problem of -valued
surjective VCSPs, we also establish a dichotomy theorem with respect to
approximability.
Unlike in the case of Boolean surjective (decision) CSPs, there appears a
novel tractable class of languages that is trivial in the non-surjective
setting. This newly discovered tractable class has an interesting mathematical
structure related to downsets and upsets. Our main contribution is identifying
this class and proving that it lies on the borderline of tractability. A
crucial part of our proof is a polynomial-time algorithm for enumerating all
near-optimal solutions to a generalised Min-Cut problem, which might be of
independent interest.Comment: v5: small corrections and improved presentatio
Success Factors of European Syndromic Surveillance Systems: A Worked Example of Applying Qualitative Comparative Analysis
Introduction: Syndromic surveillance aims at augmenting traditional public health surveillance with timely information. To gain a head start, it mainly analyses existing data such as from web searches or patient records. Despite the setup of many syndromic surveillance systems, there is still much doubt about the benefit of the approach. There are diverse interactions between performance indicators such as timeliness and various system characteristics. This makes the performance assessment of syndromic surveillance systems a complex endeavour. We assessed if the comparison of several syndromic surveillance systems through Qualitative Comparative Analysis helps to evaluate performance and identify key success factors.
Materials and Methods: We compiled case-based, mixed data on performance and characteristics of 19 syndromic surveillance systems in Europe from scientific and grey literature and from site visits. We identified success factors by applying crisp-set Qualitative Comparative Analysis. We focused on two main areas of syndromic surveillance application: seasonal influenza surveillance and situational awareness during different types of potentially health threatening events.
Results: We found that syndromic surveillance systems might detect the onset or peak of seasonal influenza earlier if they analyse non-clinical data sources. Timely situational awareness during different types of events is supported by an automated syndromic surveillance system capable of analysing multiple syndromes. To our surprise, the analysis of multiple data sources was no key success factor for situational awareness.
Conclusions: We suggest to consider these key success factors when designing or further developing syndromic surveillance systems. Qualitative Comparative Analysis helped interpreting complex, mixed data on small-N cases and resulted in concrete and practically relevant findings
Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests
We first propose algorithms for checking language equivalence of finite
automata over a large alphabet. We use symbolic automata, where the transition
function is compactly represented using a (multi-terminal) binary decision
diagrams (BDD). The key idea consists in computing a bisimulation by exploring
reachable pairs symbolically, so as to avoid redundancies. This idea can be
combined with already existing optimisations, and we show in particular a nice
integration with the disjoint sets forest data-structure from Hopcroft and
Karp's standard algorithm. Then we consider Kleene algebra with tests (KAT), an
algebraic theory that can be used for verification in various domains ranging
from compiler optimisation to network programming analysis. This theory is
decidable by reduction to language equivalence of automata on guarded strings,
a particular kind of automata that have exponentially large alphabets. We
propose several methods allowing to construct symbolic automata out of KAT
expressions, based either on Brzozowski's derivatives or standard automata
constructions. All in all, this results in efficient algorithms for deciding
equivalence of KAT expressions
An Automata Theoretic Approach to the Zero-One Law for Regular Languages: Algorithmic and Logical Aspects
A zero-one language L is a regular language whose asymptotic probability
converges to either zero or one. In this case, we say that L obeys the zero-one
law. We prove that a regular language obeys the zero-one law if and only if its
syntactic monoid has a zero element, by means of Eilenberg's variety theoretic
approach. Our proof gives an effective automata characterisation of the
zero-one law for regular languages, and it leads to a linear time algorithm for
testing whether a given regular language is zero-one. In addition, we discuss
the logical aspects of the zero-one law for regular languages.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
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