On the Computational Complexity of Reaction Systems, Revisited

2021 ◽  
pp. 170-185
Author(s):  
Markus Holzer ◽  
Christian Rauch
Keyword(s):  
Computational Complexity ◽  
Reaction Systems

scholarly journals Characterization and computation of ancestors in reaction systems

2020 ◽  
Author(s):  
Roberto Barbuti ◽  
Anna Bernasconi ◽  
Roberta Gori ◽  
Paolo Milazzo
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Boolean Formula ◽  
Minimal Size ◽  
Minimum Cardinality ◽  
Reaction Systems ◽  
Target Set ◽  
The Cost

Abstract In reaction systems, preimages and nth ancestors are sets of reactants leading to the production of a target set of products in either 1 or n steps, respectively. Many computational problems on preimages and ancestors, such as finding all minimum-cardinality nth ancestors, computing their size or counting them, are intractable. In this paper, we characterize all nth ancestors using a Boolean formula that can be computed in polynomial time. Once simplified, this formula can be exploited to easily solve all preimage and ancestor problems. This allows us to directly relate the difficulty of ancestor problems to the cost of the simplification so that new insights into computational complexity investigations can be achieved. In particular, we focus on two problems: (i) deciding whether a preimage/nth ancestor exists and (ii) finding a preimage/nth ancestor of minimal size. Our approach is constructive, it aims at finding classes of reactions systems for which the ancestor problems can be solved in polynomial time, in exact or approximate way.

EXISTENCE AND INVARIANCE FOR CONVECTION, DISPERSION, REACTION SYSTEMS WITH PRESSURE

1992 ◽  
Vol 12 (4) ◽  
pp. 443-456 ◽  
Author(s):  
Chunhong Xie ◽  
Taiping He ◽  
Guohong Bai
Keyword(s):  
Reaction Systems

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.

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