scholarly journals Decomposition-Guided Reductions for Argumentation and Treewidth

2021 ◽  
Author(s):  
Johannes Fichte ◽  
Markus Hecher ◽  
Yasir Mahmood ◽  
Arne Meier
Keyword(s):  
Computational Complexity ◽  
Lower Bounds ◽  
Complexity Analysis ◽  
Upper Bounds ◽  
Abstract Argumentation

Argumentation is a widely applied framework for modeling and evaluating arguments and its reasoning with various applications. Popular frameworks are abstract argumentation (Dung’s framework) or logic-based argumentation (Besnard-Hunter’s framework). Their computational complexity has been studied quite in-depth. Incorporating treewidth into the complexity analysis is particularly interesting, as solvers oftentimes employ SAT-based solvers, which can solve instances of low treewidth fast. In this paper, we address whether one can design reductions from argumentation problems to SAT-problems while linearly preserving the treewidth, which results in decomposition-guided (DG) reductions. It turns out that the linear treewidth overhead caused by our DG reductions, cannot be significantly improved under reasonable assumptions. Finally, we consider logic-based argumentation and establish new upper bounds using DG reductions and lower bounds.

scholarly journals Novel Algorithms for Abstract Dialectical Frameworks based on Complexity Analysis of Subclasses and SAT Solving

2018 ◽  
Author(s):  
Thomas Linsbichler ◽  
Marco Maratea ◽  
Andreas Niskanen ◽  
Johannes P. Wallner ◽  
Stefan Woltran
Keyword(s):  
Computational Complexity ◽  
Complexity Analysis ◽  
Sat Solving ◽  
Sat Solvers ◽  
Abstract Argumentation ◽  
Novel Algorithms ◽  
High Computational Complexity

Abstract dialectical frameworks (ADFs) constitute one of the most powerful formalisms in abstract argumentation. Their high computational complexity poses, however, certain challenges when designing efficient systems. In this paper, we tackle this issue by (i) analyzing the complexity of ADFs under structural restrictions, (ii) presenting novel algorithms which make use of these insights, and (iii) empirically evaluating a resulting implementation which relies on calls to SAT solvers.

scholarly journals Upper Bounds on the Complexity of Some Problems Concerning L Systems

1977 ◽  
Vol 6 (69) ◽  
Author(s):  
Neil D. Jones ◽  
Sven Skyum
Keyword(s):  
Computational Complexity ◽  
Lower Bounds ◽  
Companion Paper ◽  
Upper Bounds ◽  
Turing Machines ◽  
Lindenmayer Systems ◽  
L Systems

We determine the computational complexity of some decidable problems concerning several types of Lindenmayer systems. The problems are membership, emptiness and finiteness; the L systems are the ED0L, E0L, EDT0L and ET0L systems. For each problem and type of system we establish upper bounds on the time or memory required for solution by Turing machines. This paper contains algorithms achieving the upper bounds, and a companion paper (PB-70) contains proofs of lower bounds.

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.

scholarly journals Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

2020 ◽  
Vol 26 (2) ◽  
pp. 131-161
Author(s):  
Florian Bourgey ◽  
Stefano De Marco ◽  
Emmanuel Gobet ◽  
Alexandre Zhou
Keyword(s):  
Monte Carlo ◽  
Lower Bounds ◽  
Asymptotic Optimality ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Independent Random Variables ◽  
Outer Function ◽  
Control Problems ◽  
Multilevel Monte Carlo ◽  
Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

scholarly journals Bounding the Size and Probability of Epidemics on Networks

2008 ◽  
Vol 45 (2) ◽  
pp. 498-512 ◽  
Author(s):  
Joel C. Miller
Keyword(s):  
Infectious Disease ◽  
Lower Bounds ◽  
Upper Bounds ◽  
Marginal Probability ◽  
Transmission Properties ◽  
Disease Spreading ◽  
Special Case

We consider an infectious disease spreading along the edges of a network which may have significant clustering. The individuals in the population have heterogeneous infectiousness and/or susceptibility. We define the out-transmissibility of a node to be the marginal probability that it would infect a randomly chosen neighbor given its infectiousness and the distribution of susceptibility. For a given distribution of out-transmissibility, we find the conditions which give the upper (or lower) bounds on the size and probability of an epidemic, under weak assumptions on the transmission properties, but very general assumptions on the network. We find similar bounds for a given distribution of in-transmissibility (the marginal probability of being infected by a neighbor). We also find conditions giving global upper bounds on the size and probability. The distributions leading to these bounds are network independent. In the special case of networks with high girth (locally tree-like), we are able to prove stronger results. In general, the probability and size of epidemics are maximal when the population is homogeneous and minimal when the variance of in- or out-transmissibility is maximal.

scholarly journals The Essential Dimension of Stacks of Parabolic Vector Bundles over Curves

2012 ◽  
Vol 10 (3) ◽  
pp. 455-488 ◽  
Author(s):  
Indranil Biswas ◽  
Ajneet Dhillon ◽  
Nicole Lemire
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Vector Bundles ◽  
Upper Bounds ◽  
Essential Dimension ◽  
Parabolic Structure ◽  
Moduli Stack

AbstractWe find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our calculations also give lower bounds on the essential dimension of the semistable locus inside the moduli stack of vector bundles of rank r and degree d without parabolic structure.

scholarly journals Finding Cut-Offs in Leaderless Rendez-Vous Protocols is Easy

2021 ◽  
pp. 42-61
Author(s):  
A. R. Balasubramanian ◽  
Javier Esparza ◽  
Mikhail Raskin
Keyword(s):  
Lower Bounds ◽  
Petri Net ◽  
Special Class ◽  
Upper Bounds ◽  
Initial State ◽  
Reachability Problem ◽  
Final State ◽  
Final Configuration ◽  
Finite State ◽  
State Agents

AbstractIn rendez-vous protocols an arbitrarily large number of indistinguishable finite-state agents interact in pairs. The cut-off problem asks if there exists a number B such that all initial configurations of the protocol with at least B agents in a given initial state can reach a final configuration with all agents in a given final state. In a recent paper [17], Horn and Sangnier prove that the cut-off problem is equivalent to the Petri net reachability problem for protocols with a leader, and in "Image missing" for leaderless protocols. Further, for the special class of symmetric protocols they reduce these bounds to "Image missing" and "Image missing" , respectively. The problem of lowering these upper bounds or finding matching lower bounds is left open. We show that the cut-off problem is "Image missing" -complete for leaderless protocols, "Image missing" -complete for symmetric protocols with a leader, and in "Image missing" for leaderless symmetric protocols, thereby solving all the problems left open in [17].

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