scholarly journals Complexity of some Problems Concerning L Systems. (Preliminary report)

1976 ◽  
Vol 5 (67) ◽  
Author(s):  
Neil D. Jones
Keyword(s):  
Computational Complexity ◽  
Lower Bounds ◽  
Preliminary Report ◽  
Upper And Lower Bounds ◽  
Turing Machines ◽  
L Systems

We study the computational complexity of some decidable 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 state both upper and lower bounds on the time or memory required for solution by Turing machines. Two following papers (PB-69 and PB70) will contain detailed constructions and proofs for the upper and lower bounds.

scholarly journals Complexity of Some Problems Concerning Lindenmayer Systems. (Revised version)

1979 ◽  
Vol 7 (85) ◽  
Author(s):  
Neil D. Jones ◽  
Sven Skyum
Keyword(s):  
Computational Complexity ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Turing Machines ◽  
Lindenmayer Systems ◽  
L Systems

<p>We determine the computational complexity of membership, emptiness and infiniteness for several types of L systems. The L systems we consider are EDOL, EOL, EDTOL, and ETOL, with and without empty productions. For each problem and each type of system we establish both upper and lower bounds on the time or memory required for solution by Turing machines.</p><p>Revised version (first version 1978 under the title <em>Complexity of Some Problems Concerning: Lindenmayer Systems</em>)</p>

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.

scholarly journals Simplified group activity selection with group size constraints

2021 ◽  
Author(s):  
Andreas Darmann ◽  
Janosch Döcker ◽  
Britta Dorn ◽  
Sebastian Schneckenburger
Keyword(s):  
Computational Complexity ◽  
Simple Model ◽  
Lower Bounds ◽  
Group Activity ◽  
Core Stability ◽  
Upper And Lower Bounds ◽  
Size Constraints ◽  
Broad Variety ◽  
Special Case ◽  
Additional Constraints

AbstractSeveral real-world situations can be represented in terms of agents that have preferences over activities in which they may participate. Often, the agents can take part in at most one activity (for instance, since these take place simultaneously), and there are additional constraints on the number of agents that can participate in an activity. In such a setting, we consider the task of assigning agents to activities in a reasonable way. We introduce the simplified group activity selection problem providing a general yet simple model for a broad variety of settings, and start investigating its special case where upper and lower bounds of the groups have to be taken into account. We apply different solution concepts such as envy-freeness and core stability to our setting and provide a computational complexity study for the problem of finding such solutions.

The Travelling Salesman Problem in symmetric circulant matrices with two stripes

2008 ◽  
Vol 18 (1) ◽  
pp. 165-175 ◽  
Author(s):  
IVAN GERACE ◽  
FEDERICO GRECO
Keyword(s):  
Computational Complexity ◽  
Lower Bound ◽  
Lower Bounds ◽  
Travelling Salesman Problem ◽  
Minimum Cost ◽  
Circulant Matrix ◽  
Upper And Lower Bounds ◽  
Circulant Matrices ◽  
Travelling Salesman ◽  
New Construction

The Symmetric Circulant Travelling Salesman Problem asks for the minimum cost tour in a symmetric circulant matrix. The computational complexity of this problem is not known – only upper and lower bounds have been determined. This paper provides a characterisation of the two-stripe case. Instances where the minimum cost of a tour is equal to either the upper or lower bound are recognised. A new construction providing a tour is proposed for the remaining instances, and this leads to a new upper bound that is closer than the previous one.

scholarly journals A Note on the Complexity of General D0L Membership

1979 ◽  
Vol 8 (93) ◽  
Author(s):  
Neil D. Jones
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Upper And Lower Bounds ◽  
Membership Problem ◽  
L Systems

A number of upper and lower bounds have been obtained for various problems concerning L systems (see PB-85). In most cases the bounds were rather close; however, for the general membership problem the upper bound was P, and the lower was deterministic log space. In this note we show that membership can be decided deterministically in log^2 n space, which makes it very unlikely that the problem is complete for P. We also show that non-membership is as hard as any problem solvable in nondeterministic log n space. Thus both bounds are improved.

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

1977 ◽  
Vol 6 (70) ◽  
Author(s):  
Neil D. Jones ◽  
Sven Skyum
Keyword(s):  
Lower Bounds ◽  
Preceding Paper ◽  
Upper Bounds ◽  
Turing Machines ◽  
Lindenmayer Systems ◽  
L Systems

This is the second of two papers on the complexity of deciding membership, emptiness and finiteness of four basic types of Lindenmayer systems: the ED0L, E0L, EDT0L and ET0L systems. For each problem and type of system we establish lower bounds on the time or memory required for solution by Turing machines, using reducibility techniques. These bounds, combined with the upper bounds of the preceding paper, show many of these problems to be complete for NP or PSPACE.

scholarly journals False-Name Manipulations in Weighted Voting Games

2011 ◽  
Vol 40 ◽  
pp. 57-93 ◽  
Author(s):  
H. Aziz ◽  
Y. Bachrach ◽  
E. Elkind ◽  
M. Paterson
Keyword(s):  
Decision Making ◽  
Computational Complexity ◽  
Lower Bounds ◽  
Experimental Evaluation ◽  
Randomized Algorithms ◽  
Power Index ◽  
Upper And Lower Bounds ◽  
Banzhaf Index ◽  
Weighted Voting ◽  
Voting Games

Weighted voting is a classic model of cooperation among agents in decision-making domains. In such games, each player has a weight, and a coalition of players wins the game if its total weight meets or exceeds a given quota. A player's power in such games is usually not directly proportional to his weight, and is measured by a power index, the most prominent among which are the Shapley-Shubik index and the Banzhaf index.In this paper, we investigate by how much a player can change his power, as measured by the Shapley-Shubik index or the Banzhaf index, by means of a false-name manipulation, i.e., splitting his weight among two or more identities. For both indices, we provide upper and lower bounds on the effect of weight-splitting. We then show that checking whether a beneficial split exists is NP-hard, and discuss efficient algorithms for restricted cases of this problem, as well as randomized algorithms for the general case. We also provide an experimental evaluation of these algorithms. Finally, we examine related forms of manipulative behavior, such as annexation, where a player subsumes other players, or merging, where several players unite into one. We characterize the computational complexity of such manipulations and provide limits on their effects. For the Banzhaf index, we describe a new paradox, which we term the Annexation Non-monotonicity Paradox.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

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