37,314 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
Self-Replicating Machines in Continuous Space with Virtual Physics
JohnnyVon is an implementation of self-replicating machines in
continuous two-dimensional space. Two types of particles drift
about in a virtual liquid. The particles are automata with
discrete internal states but continuous external relationships.
Their internal states are governed by finite state machines but
their external relationships are governed by a simulated physics
that includes Brownian motion, viscosity, and spring-like attractive
and repulsive forces. The particles can be assembled into patterns
that can encode arbitrary strings of bits. We demonstrate that, if
an arbitrary "seed" pattern is put in a "soup" of separate individual
particles, the pattern will replicate by assembling the individual
particles into copies of itself. We also show that, given sufficient
time, a soup of separate individual particles will eventually
spontaneously form self-replicating patterns. We discuss the implications
of JohnnyVon for research in nanotechnology, theoretical biology, and
artificial life
Quantitative model checking of continuous-time Markov chains against timed automata specifications
We study the following problem: given a continuous-time Markov chain (CTMC) C, and a linear real-time property provided as a deterministic timed automaton (DTA) A, what is the probability of the set of paths of C that are\ud
accepted by A (C satisfies A)? It is shown that this set of paths is measurable and computing its probability can be reduced to computing the reachability probability in a piecewise deterministic Markov process (PDP). The reachability probability is characterized as the least solution of a system of integral equations and is shown to be approximated by solving a system of partial differential equations. For the special case of single-clock DTA, the system of integral equations can be transformed into a system of linear equations where the coefficients are solutions of ordinary differential equations
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