29,634 research outputs found
Efficient universal pushdown cellular automata and their application to complexity
In order to obtain universal classical cellular automata an infinite space is required. Therefore, the number of required processors depends on the length of input data and, additionally, may increase during the computation. On the other hand, Turing machines are universal devices which have one processor only and additionally an infinite storage tape.
Here an in some sense intermediate model is studied. The pushdown cellular automata are a stack augmented generalization of classical cellular automata. They form a massively parallel universal model where the number of processors is bounded by the length of input data.
Effcient universal pushdown cellular automata and their efficiently verifiable encodings are proposed. They are applied to computational complexity, and tight time and stack-space hierarchies are shown.
CR Subject Classification (1998): F.1, F.4.3, B.6.1, E.
Simulation of Two-Way Pushdown Automata Revisited
The linear-time simulation of 2-way deterministic pushdown automata (2DPDA)
by the Cook and Jones constructions is revisited. Following the semantics-based
approach by Jones, an interpreter is given which, when extended with
random-access memory, performs a linear-time simulation of 2DPDA. The recursive
interpreter works without the dump list of the original constructions, which
makes Cook's insight into linear-time simulation of exponential-time automata
more intuitive and the complexity argument clearer. The simulation is then
extended to 2-way nondeterministic pushdown automata (2NPDA) to provide for a
cubic-time recognition of context-free languages. The time required to run the
final construction depends on the degree of nondeterminism. The key mechanism
that enables the polynomial-time simulations is the sharing of computations by
memoization.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455
Program schemes with deep pushdown storage.
Inspired by recent work of Meduna on deep pushdown automata, we consider the computational power of a class of basic program schemes, TeX, based around assignments, while-loops and non- deterministic guessing but with access to a deep pushdown stack which, apart from having the usual push and pop instructions, also has deep-push instructions which allow elements to be pushed to stack locations deep within the stack. We syntactically define sub-classes of TeX by restricting the occurrences of pops, pushes and deep-pushes and capture the complexity classes NP and PSPACE. Furthermore, we show that all problems accepted by program schemes of TeX are in EXPTIME
On space efficiency of algorithms working on structural decompositions of graphs
Dynamic programming on path and tree decompositions of graphs is a technique
that is ubiquitous in the field of parameterized and exponential-time
algorithms. However, one of its drawbacks is that the space usage is
exponential in the decomposition's width. Following the work of Allender et al.
[Theory of Computing, '14], we investigate whether this space complexity
explosion is unavoidable. Using the idea of reparameterization of Cai and
Juedes [J. Comput. Syst. Sci., '03], we prove that the question is closely
related to a conjecture that the Longest Common Subsequence problem
parameterized by the number of input strings does not admit an algorithm that
simultaneously uses XP time and FPT space. Moreover, we complete the complexity
landscape sketched for pathwidth and treewidth by Allender et al. by
considering the parameter tree-depth. We prove that computations on tree-depth
decompositions correspond to a model of non-deterministic machines that work in
polynomial time and logarithmic space, with access to an auxiliary stack of
maximum height equal to the decomposition's depth. Together with the results of
Allender et al., this describes a hierarchy of complexity classes for
polynomial-time non-deterministic machines with different restrictions on the
access to working space, which mirrors the classic relations between treewidth,
pathwidth, and tree-depth.Comment: An extended abstract appeared in the proceedings of STACS'16. The new
version is augmented with a space-efficient algorithm for Dominating Set
using the Chinese remainder theore
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