908 research outputs found
A Generalised Twinning Property for Minimisation of Cost Register Automata
Weighted automata (WA) extend finite-state automata by associating with transitions weights from a semiring S, defining functions from words to S. Recently, cost register automata (CRA) have been introduced as an alternative model to describe any function realised by a WA by means of a deterministic machine. Unambiguous WA over a monoid (M, â) can equivalently be described by cost register automata whose registers take their values in M, and are updated by operations of the form x: = y â c, with c â M. This class is denoted by CRAâc(M).
We introduce a twinning property and a bounded variation property parametrised by an integer k, such that the corresponding notions introduced originally by Choffrut for finite-state transducers are obtained for k = 1. Given an unambiguous weighted automaton W over an infinitary group (G, â) realizing some function f, we prove that the three following properties are equivalent: i) W satisfies the twinning property of order k, ii) f satisfies the k-bounded variation property, and iii) f can be described by a CRAâc(G) with at most k registers.
In the spirit of tranducers, we actually prove this result in a more general setting by considering machines over the semiring of finite sets of elements from (G, â): the three properties are still equivalent for such finite-valued weighted automata, that is the ones associating with words subsets of G of cardinality at most â, for some natural â. Moreover, we show that if the operation â of G is commutative and computable, then one can decide whether a WA satisfies the twinning property of order k. As a corollary, this allows to decide the register minimisation problem for the class CRAâc(G).
Last, we prove that a similar result holds for finite-valued finite-state transducers, and that the register minimisation problem for the class CRA.c (B*) is Pspace-complete
Size-Change Abstraction and Max-Plus Automata
Max-plus automata (over â âȘââââ) are finite devices that map input words to non-negative integers or âââ. In this paper we present (a) an algorithm allowing to compute the asymptotic behaviour of max-plus automata, and (b) an application of this technique to the evaluation of the computational time complexity of programs
The Reversed q-Exponential Functional Relation
After obtaining some useful identities, we prove an additional functional
relation for exponentials with reversed order of multiplication, as well as
the well known direct one in a completely rigorous manner.Comment: 6 pages, LaTeX, no figure
Noncommutative Hypergeometry
A certain special function of the generalized hypergeometric variety is shown
to fulfill a host of useful noncommutative identities.Comment: 14 pages, LaTeX (amsart
An automata characterisation for multiple context-free languages
We introduce tree stack automata as a new class of automata with storage and
identify a restricted form of tree stack automata that recognises exactly the
multiple context-free languages.Comment: This is an extended version of a paper with the same title accepted
at the 20th International Conference on Developments in Language Theory (DLT
2016
Aperiodic String Transducers
Regular string-to-string functions enjoy a nice triple characterization
through deterministic two-way transducers (2DFT), streaming string transducers
(SST) and MSO definable functions. This result has recently been lifted to FO
definable functions, with equivalent representations by means of aperiodic 2DFT
and aperiodic 1-bounded SST, extending a well-known result on regular
languages. In this paper, we give three direct transformations: i) from
1-bounded SST to 2DFT, ii) from 2DFT to copyless SST, and iii) from k-bounded
to 1-bounded SST. We give the complexity of each construction and also prove
that they preserve the aperiodicity of transducers. As corollaries, we obtain
that FO definable string-to-string functions are equivalent to SST whose
transition monoid is finite and aperiodic, and to aperiodic copyless SST
- âŠ