66,349 research outputs found
Single-Elimination Brackets Fail to Approximate Copeland Winner
Single-elimination (SE) brackets appear commonly in both sports tournaments and the voting theory literature. In certain tournament models, they have been shown to select the unambiguously-strongest competitor with optimum probability. By contrast, we reevaluate SE brackets through the lens of approximation, where the goal is to select a winner who would beat the most other competitors in a round robin (i.e., maximize the Copeland score), and find them lacking. Our primary result establishes the approximation ratio of a randomly-seeded SE bracket is 2^{- Theta(sqrt{log n})}; this is underwhelming considering a 1/2 ratio is achieved by choosing a winner uniformly at random. We also establish that a generalized version of the SE bracket performs nearly as poorly, with an approximation ratio of 2^{- Omega(sqrt[4]{log n})}, addressing a decade-old open question in the voting tree literature
Compositional Algorithms for Succinct Safety Games
We study the synthesis of circuits for succinct safety specifications given
in the AIG format. We show how AIG safety specifications can be decomposed
automatically into sub specifications. Then we propose symbolic compositional
algorithms to solve the synthesis problem compositionally starting for the
sub-specifications. We have evaluated the compositional algorithms on a set of
benchmarks including those proposed for the first synthesis competition
organised in 2014 by the Synthesis Workshop affiliated to the CAV conference.
We show that a large number of benchmarks can be decomposed automatically and
solved more efficiently with the compositional algorithms that we propose in
this paper.Comment: In Proceedings SYNT 2015, arXiv:1602.0078
Dynamics of Three Agent Games
We study the dynamics and resulting score distribution of three-agent games
where after each competition a single agent wins and scores a point. A single
competition is described by a triplet of numbers , and denoting the
probabilities that the team with the highest, middle or lowest accumulated
score wins. We study the full family of solutions in the regime, where the
number of agents and competitions is large, which can be regarded as a
hydrodynamic limit. Depending on the parameter values , we find six
qualitatively different asymptotic score distributions and we also provide a
qualitative understanding of these results. We checked our analytical results
against numerical simulations of the microscopic model and find these to be in
excellent agreement. The three agent game can be regarded as a social model
where a player can be favored or disfavored for advancement, based on his/her
accumulated score. It is also possible to decide the outcome of a three agent
game through a mini tournament of two-a gent competitions among the
participating players and it turns out that the resulting possible score
distributions are a subset of those obtained for the general three agent-games.
We discuss how one can add a steady and democratic decline rate to the model
and present a simple geometric construction that allows one to write down the
corresponding score evolution equations for -agent games
Dynamics of Three Agent Games
We study the dynamics and resulting score distribution of three-agent games
where after each competition a single agent wins and scores a point. A single
competition is described by a triplet of numbers , and denoting the
probabilities that the team with the highest, middle or lowest accumulated
score wins. We study the full family of solutions in the regime, where the
number of agents and competitions is large, which can be regarded as a
hydrodynamic limit. Depending on the parameter values , we find six
qualitatively different asymptotic score distributions and we also provide a
qualitative understanding of these results. We checked our analytical results
against numerical simulations of the microscopic model and find these to be in
excellent agreement. The three agent game can be regarded as a social model
where a player can be favored or disfavored for advancement, based on his/her
accumulated score. It is also possible to decide the outcome of a three agent
game through a mini tournament of two-a gent competitions among the
participating players and it turns out that the resulting possible score
distributions are a subset of those obtained for the general three agent-games.
We discuss how one can add a steady and democratic decline rate to the model
and present a simple geometric construction that allows one to write down the
corresponding score evolution equations for -agent games
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