240,000 research outputs found
Benchmarks for Parity Games (extended version)
We propose a benchmark suite for parity games that includes all benchmarks
that have been used in the literature, and make it available online. We give an
overview of the parity games, including a description of how they have been
generated. We also describe structural properties of parity games, and using
these properties we show that our benchmarks are representative. With this work
we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from
https://github.com/jkeiren/paritygame-generator. This is an extended version
of the paper that has been accepted for FSEN 201
Stable Marriage with Ties and Bounded Length Preference Lists
We consider variants of the classical stable marriage problem in which preference lists may contain ties, and may be of bounded length. Such restrictions arise naturally in practical applications, such as centralised matching schemes that assign graduating medical students to their first hospital posts. In such a setting, weak stability is the most common solution concept, and it is known that weakly stable matchings can have different sizes. This motivates the problem of finding a maximum cardinality weakly stable matching, which is known to be NP-hard in general. We show that this problem is solvable in polynomial time if each man's list is of length at most 2 (even for women's lists that are of unbounded length). However if each man's list is of length at most 3, we show that the problem becomes NP-hard and not approximable within some d > 1, even if each woman's list is of length at most 4
Stable marriage with ties and bounded length preference lists
We consider variants of the classical stable marriage problem in which preference lists may contain ties, and may be of bounded length. Such restrictions arise naturally in practical applications, such as centralised matching schemes that assign graduating medical students to their first hospital posts. In such a setting, weak stability is the most common solution concept, and it is known that weakly stable matchings can have different sizes. This motivates the problem of finding a maximum cardinality weakly stable matching, which is known to be NP-hard in general. We show that this problem is solvable in polynomial time if each man's list is of length at most 2 (even for women's lists that are of unbounded length). However if each man's list is of length at most 3, we show that the problem becomes NP-hard (even if each women's list is of length at most 3) and not approximable within some δ>1 (even if each woman's list is of length at most 4)
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
Approximation algorithms for hard variants of the stable marriage and hospitals/residents problems
When ties and incomplete preference lists are permitted in the Stable Marriage and Hospitals/Residents problems, stable matchings can have different sizes. The problem of finding a maximum cardinality stable matching in this context is known to be NP-hard, even under very severe restrictions on the number, size and position of ties. In this paper, we describe polynomial-time 5/3-approximation algorithms for variants of these problems in which ties are on one side only and at the end of the preference lists. The particular variant is motivated by important applications in large scale centralised matching schemes
Complexity of Restricted and Unrestricted Models of Molecular Computation
In [9] and [2] a formal model for molecular computing was
proposed, which makes focused use of affinity purification.
The use of PCR was suggested to expand the range of
feasible computations, resulting in a second model. In this
note, we give a precise characterization of these two models
in terms of recognized computational complexity classes,
namely branching programs (BP) and nondeterministic
branching programs (NBP) respectively. This allows us to
give upper and lower bounds on the complexity of desired
computations. Examples are given of computable and
uncomputable problems, given limited time
Local Sentences and Mahlo Cardinals
Local sentences were introduced by J.-P. Ressayre who proved certain
remarkable stretching theorems establishing the equivalence between the
existence of finite models for these sentences and the existence of some
infinite well ordered models. Two of these stretching theorems were only proved
under certain large cardinal axioms but the question of their exact
(consistency) strength was left open in [O. Finkel and J.-P. Ressayre,
Stretchings, Journal of Symbolic Logic, Volume 61 (2), 1996, p. 563-585 ].
Here, we solve this problem, using a combinatorial result of J. H. Schmerl. In
fact, we show that the stretching principles are equivalent to the existence of
n-Mahlo cardinals for appropriate integers n. This is done by proving first
that for each integer n, there is a local sentence phi_n which has well ordered
models of order type alpha, for every infinite ordinal alpha > omega which is
not an n-Mahlo cardinal
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