5,846 research outputs found
A Computation in a Cellular Automaton Collider Rule 110
A cellular automaton collider is a finite state machine build of rings of
one-dimensional cellular automata. We show how a computation can be performed
on the collider by exploiting interactions between gliders (particles,
localisations). The constructions proposed are based on universality of
elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and
computing on rings.Comment: 39 pages, 32 figures, 3 table
Representations of Circular Words
In this article we give two different ways of representations of circular
words. Representations with tuples are intended as a compact notation, while
representations with trees give a way to easily process all conjugates of a
word. The latter form can also be used as a graphical representation of
periodic properties of finite (in some cases, infinite) words. We also define
iterative representations which can be seen as an encoding utilizing the
flexible properties of circular words. Every word over the two letter alphabet
can be constructed starting from ab by applying the fractional power and the
cyclic shift operators one after the other, iteratively.Comment: In Proceedings AFL 2014, arXiv:1405.527
Memoization for Unary Logic Programming: Characterizing PTIME
We give a characterization of deterministic polynomial time computation based
on an algebraic structure called the resolution semiring, whose elements can be
understood as logic programs or sets of rewriting rules over first-order terms.
More precisely, we study the restriction of this framework to terms (and logic
programs, rewriting rules) using only unary symbols. We prove it is complete
for polynomial time computation, using an encoding of pushdown automata. We
then introduce an algebraic counterpart of the memoization technique in order
to show its PTIME soundness. We finally relate our approach and complexity
results to complexity of logic programming. As an application of our
techniques, we show a PTIME-completeness result for a class of logic
programming queries which use only unary function symbols.Comment: Soumis {\`a} LICS 201
- …