2 research outputs found
Finite Automata With Restricted Two-Way Motion
We consider finite two-way automata and measure the use of two-way motion by
counting the number of left moves in accepting computations. Restriction of the
automata according to this measure allows us to study in detail the use of
two-way motion for the acceptance of regular languages in terms of state
complexity. The two-way spectrum of a given regular language is introduced.
This quantity reflects the change of size of minimal accepting devices if the
use of two-way motion is increased incrementally. We give examples for spectra,
prove uniform upper and lower bounds and study their sharpness. We also have
state complexity results for two-way automata with uniformly bounded use of
two-way motion.Comment: 21 page
Symmetries and transitions of bounded Turing machines
We consider the structures given by repeatedly generalising the definition of
finite state automata by symmetry considerations, and constructing analogues of
transition monoids at each step. This approach first gives us non-deterministic
automata, then (non-deterministic) two-way automata and bounded Turing machines
--- that is, Turing machines where the read / write head is unable to move past
the end of the input word.
In the case of two-way automata, the transition monoids generalise to
endomorphism monoids in compact closed categories. These use Girard's
resolution formula (from the Geometry of Interaction representation of linear
logic) to construct the images of singleton words.
In the case of bounded Turing machines, the transition homomorphism
generalises to a monoid homomorphism from the natural numbers to a monoid
constructed from the union of endomorphism monoids of a compact closed
category, together with an appropriate composition. These use Girard's
execution formula (also from the Geometry of Interaction representation of
linear logic) to construct images of singletons.Comment: 21 pages, submitte