scholarly journals Best-Effort Synthesis: Doing Your Best Is Not Harder Than Giving Up

2021 ◽  
Author(s):  
Benjamin Aminof ◽  
Giuseppe De Giacomo ◽  
Sasha Rubin
Keyword(s):  
Computational Complexity ◽  
Optimal Algorithms ◽  
Best Effort ◽  
Ltl Synthesis

We study best-effort synthesis under environment assumptions specified in LTL, and show that this problem has exactly the same computational complexity of standard LTL synthesis: 2EXPTIME-complete. We provide optimal algorithms for computing best-effort strategies, both in the case of LTL over infinite traces and LTL over finite traces (i.e., LTLf). The latter are particularly well suited for implementation.

scholarly journals Synthesizing Best-effort Strategies under Multiple Environment Specifications

2021 ◽  
Author(s):  
Benjamin Aminof ◽  
Giuseppe De Giacomo ◽  
Alessio Lomuscio ◽  
Aniello Murano ◽  
Sasha Rubin
Keyword(s):  
Solution Concept ◽  
Important Case ◽  
Synthesis Problem ◽  
Best Effort ◽  
Ltl Synthesis ◽  
Multiple Environments ◽  
Theoretic Characterization

We formally introduce and solve the synthesis problem for LTL goals in the case of multiple, even contradicting, assumptions about the environment. Our solution concept is based on ``best-effort strategies'' which are agent plans that, for each of the environment specifications individually, achieve the agent goal against a maximal set of environments satisfying that specification. By means of a novel automata theoretic characterization we demonstrate that this best-effort synthesis for multiple environments is 2ExpTime-complete, i.e., no harder than plain LTL synthesis. We study an important case in which the environment specifications are increasingly indeterminate, and show that as in the case of a single environment, best-effort strategies always exist for this setting. Moreover, we show that in this setting the set of solutions are exactly the strategies formed as follows: amongst the best-effort agent strategies for ɸ under the environment specification E1, find those that do a best-effort for ɸ under (the more indeterminate) environment specification E2, and amongst those find those that do a best-effort for ɸ under the environment specification E3, etc.

Bipolar Abstract Argumentation with Dual Attacks and Supports

2020 ◽  
Author(s):  
Nico Potyka
Keyword(s):  
Computational Complexity ◽  
Decision Problems ◽  
Abstract Argumentation ◽  
Stable Semantics ◽  
Support Relations ◽  
Support Relationships ◽  
Computational Properties ◽  
Inherent Tendency

Bipolar abstract argumentation frameworks allow modeling decision problems by defining pro and contra arguments and their relationships. In some popular bipolar frameworks, there is an inherent tendency to favor either attack or support relationships. However, for some applications, it seems sensible to treat attack and support equally. Roughly speaking, turning an attack edge into a support edge, should just invert its meaning. We look at a recently introduced bipolar argumentation semantics and two novel alternatives and discuss their semantical and computational properties. Interestingly, the two novel semantics correspond to stable semantics if no support relations are present and maintain the computational complexity of stable semantics in general bipolar frameworks.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

Fat Computational Complexity and Heuristic Design for the TSP

2009 ◽  
Vol 20 (9) ◽  
pp. 2344-2351 ◽  
Author(s):  
He JIANG ◽  
Yan HU ◽  
Qiang LI ◽  
Hong YU
Keyword(s):  
Computational Complexity
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