7,416 research outputs found
One-Tape Turing Machine Variants and Language Recognition
We present two restricted versions of one-tape Turing machines. Both
characterize the class of context-free languages. In the first version,
proposed by Hibbard in 1967 and called limited automata, each tape cell can be
rewritten only in the first visits, for a fixed constant .
Furthermore, for deterministic limited automata are equivalent to
deterministic pushdown automata, namely they characterize deterministic
context-free languages. Further restricting the possible operations, we
consider strongly limited automata. These models still characterize
context-free languages. However, the deterministic version is less powerful
than the deterministic version of limited automata. In fact, there exist
deterministic context-free languages that are not accepted by any deterministic
strongly limited automaton.Comment: 20 pages. This article will appear in the Complexity Theory Column of
the September 2015 issue of SIGACT New
Reactive Turing Machines
We propose reactive Turing machines (RTMs), extending classical Turing
machines with a process-theoretical notion of interaction, and use it to define
a notion of executable transition system. We show that every computable
transition system with a bounded branching degree is simulated modulo
divergence-preserving branching bisimilarity by an RTM, and that every
effective transition system is simulated modulo the variant of branching
bisimilarity that does not require divergence preservation. We conclude from
these results that the parallel composition of (communicating) RTMs can be
simulated by a single RTM. We prove that there exist universal RTMs modulo
branching bisimilarity, but these essentially employ divergence to be able to
simulate an RTM of arbitrary branching degree. We also prove that modulo
divergence-preserving branching bisimilarity there are RTMs that are universal
up to their own branching degree. Finally, we establish a correspondence
between executability and finite definability in a simple process calculus
Measurement-Based Quantum Turing Machines and Questions of Universalities
Quantum measurement is universal for quantum computation. This universality
allows alternative schemes to the traditional three-step organisation of
quantum computation: initial state preparation, unitary transformation,
measurement. In order to formalize these other forms of computation, while
pointing out the role and the necessity of classical control in
measurement-based computation, and for establishing a new upper bound of the
minimal resources needed to quantum universality, a formal model is introduced
by means of Measurement-based Quantum Turing Machines.Comment: 12 pages, 9 figure
Temperature 1 Self-Assembly: Deterministic Assembly in 3D and Probabilistic Assembly in 2D
We investigate the power of the Wang tile self-assembly model at temperature
1, a threshold value that permits attachment between any two tiles that share
even a single bond. When restricted to deterministic assembly in the plane, no
temperature 1 assembly system has been shown to build a shape with a tile
complexity smaller than the diameter of the shape. In contrast, we show that
temperature 1 self-assembly in 3 dimensions, even when growth is restricted to
at most 1 step into the third dimension, is capable of simulating a large class
of temperature 2 systems, in turn permitting the simulation of arbitrary Turing
machines and the assembly of squares in near optimal
tile complexity. Further, we consider temperature 1 probabilistic assembly in
2D, and show that with a logarithmic scale up of tile complexity and shape
scale, the same general class of temperature systems can be simulated
with high probability, yielding Turing machine simulation and
assembly of squares with high probability. Our results show a sharp
contrast in achievable tile complexity at temperature 1 if either growth into
the third dimension or a small probability of error are permitted. Motivated by
applications in nanotechnology and molecular computing, and the plausibility of
implementing 3 dimensional self-assembly systems, our techniques may provide
the needed power of temperature 2 systems, while at the same time avoiding the
experimental challenges faced by those systems
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