14,725 research outputs found
Instruction sequence size complexity of parity
Each Boolean function can be computed by a single-pass instruction sequence
that contains only instructions to set and get the content of Boolean
registers, forward jump instructions, and a termination instruction. Auxiliary
Boolean registers are not necessary for this. In the current paper, we show
that, in the case of the parity functions, shorter instruction sequences are
possible with the use of an auxiliary Boolean register in the presence of
instructions to complement the content of auxiliary Boolean registers. This
result supports, in a setting where programs are instruction sequences acting
on Boolean registers, a basic intuition behind the storage of auxiliary data,
namely the intuition that this makes possible a reduction of the size of a
program.Comment: 12 pages, the preliminaries are largely the same as the preliminaries
in arXiv:1312.1812 [cs.PL] and some earlier papers; 13 pages, minor errors
corrected; 13 pages, presentation improved; 14 pages, remarks about related
work added; 14 pages, presentation improve
Quantitative Expressiveness of Instruction Sequence Classes for Computation on Single Bit Registers
The number of instructions of an instruction sequence is taken for its
logical SLOC, and is abbreviated with LLOC. A notion of quantitative
expressiveness is based on LLOC and in the special case of operation over a
family of single bit registers a collection of elementary properties are
established. A dedicated notion of interface is developed and is used for
stating relevant properties of classes of instruction sequence
The Computational Complexity of Generating Random Fractals
In this paper we examine a number of models that generate random fractals.
The models are studied using the tools of computational complexity theory from
the perspective of parallel computation. Diffusion limited aggregation and
several widely used algorithms for equilibrating the Ising model are shown to
be highly sequential; it is unlikely they can be simulated efficiently in
parallel. This is in contrast to Mandelbrot percolation that can be simulated
in constant parallel time. Our research helps shed light on the intrinsic
complexity of these models relative to each other and to different growth
processes that have been recently studied using complexity theory. In addition,
the results may serve as a guide to simulation physics.Comment: 28 pages, LATEX, 8 Postscript figures available from
[email protected]
On the time complexity of 2-tag systems and small universal Turing machines
We show that 2-tag systems efficiently simulate Turing machines. As a
corollary we find that the small universal Turing machines of Rogozhin, Minsky
and others simulate Turing machines in polynomial time. This is an exponential
improvement on the previously known simulation time overhead and improves a
forty year old result in the area of small universal Turing machines.Comment: Slightly expanded and updated from conference versio
The Complexity of Nash Equilibria in Simple Stochastic Multiplayer Games
We analyse the computational complexity of finding Nash equilibria in simple
stochastic multiplayer games. We show that restricting the search space to
equilibria whose payoffs fall into a certain interval may lead to
undecidability. In particular, we prove that the following problem is
undecidable: Given a game G, does there exist a pure-strategy Nash equilibrium
of G where player 0 wins with probability 1. Moreover, this problem remains
undecidable if it is restricted to strategies with (unbounded) finite memory.
However, if mixed strategies are allowed, decidability remains an open problem.
One way to obtain a provably decidable variant of the problem is restricting
the strategies to be positional or stationary. For the complexity of these two
problems, we obtain a common lower bound of NP and upper bounds of NP and
PSPACE respectively.Comment: 23 pages; revised versio
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