1,202 research outputs found
Planar digraphs for automatic complexity
We show that the digraph of a nondeterministic finite automaton witnessing
the automatic complexity of a word can always be taken to be planar. In the
case of total transition functions studied by Shallit and Wang, planarity can
fail.
Let be the number of binary words of length having
nondeterministic automatic complexity . We show that is
eventually constant for each and that the eventual constant value of
is computable.Comment: Theory and Applications of Models of Computation (TAMC 2019), Lecture
Notes in Computer Science 11436 (2019
Space Lower Bounds for Graph Stream Problems
This work concerns with proving space lower bounds for graph problems in the
streaming model. It is known that computing the length of shortest path between
two nodes in the streaming model requires space, where is the
number of nodes in the graph. We study the problem of finding the depth of a
given node in a rooted tree in the streaming model. For this problem we prove a
tight single pass space lower bound and a multipass space lower bound. As this
is a special case of computing shortest paths on graphs, the above lower bounds
also apply to the shortest path problem in the streaming model. The results are
obtained by using known communication complexity lower bounds or by
constructing hard instances for the problem. Additionally, we apply the
techniques used in proving the above lower bound results to prove space lower
bounds (single and multipass) for other graph problems like finding min
cut, detecting negative weight cycle and finding whether two nodes lie in the
same strongly connected component.Comment: Published in the conference on. Theory and Applications of Models of
Computation (TAMC) 2019 pp 635-64
Different Approaches to Proof Systems
The classical approach to proof complexity perceives proof systems as deterministic, uniform, surjective, polynomial-time computable functions that map strings to (propositional) tautologies. This approach has been intensively studied since the late 70’s and a lot of progress has been made. During the last years research was started investigating alternative notions of proof systems. There are interesting results stemming from dropping the uniformity requirement, allowing oracle access, using quantum computations, or employing probabilism. These lead to different notions of proof systems for which we survey recent results in this paper
Logical closure properties of propositional proof systems - (Extended abstract)
In this paper we define and investigate basic logical closure properties of propositional proof systems such as closure of arbitrary proof systems under modus ponens or substitutions. As our main result we obtain a purely logical characterization of the degrees of schematic extensions of EF in terms of a simple combination of these properties. This result underlines the empirical evidence that EF and its extensions admit a robust definition which rests on only a few central concepts from propositional logic
Pseudo-Hermitian continuous-time quantum walks
In this paper we present a model exhibiting a new type of continuous-time
quantum walk (as a quantum mechanical transport process) on networks, which is
described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it
pseudo-Hermitian continuous-time quantum walk. We introduce a method to obtain
the probability distribution of walk on any vertex and then study a specific
system. We observe that the probability distribution on certain vertices
increases compared to that of the Hermitian case. This formalism makes the
transport process faster and can be useful for search algorithms.Comment: 13 page, 7 figure
Sensitivity Conjecture and Log-rank Conjecture for functions with small alternating numbers
The Sensitivity Conjecture and the Log-rank Conjecture are among the most
important and challenging problems in concrete complexity. Incidentally, the
Sensitivity Conjecture is known to hold for monotone functions, and so is the
Log-rank Conjecture for and with monotone
functions , where and are bit-wise AND and XOR,
respectively. In this paper, we extend these results to functions which
alternate values for a relatively small number of times on any monotone path
from to . These deepen our understandings of the two conjectures,
and contribute to the recent line of research on functions with small
alternating numbers
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