280,175 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
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
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
Mathematical models of avascular cancer
This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions
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
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