2,167 research outputs found
Generalized Results on Monoids as Memory
We show that some results from the theory of group automata and monoid
automata still hold for more general classes of monoids and models. Extending
previous work for finite automata over commutative groups, we demonstrate a
context-free language that can not be recognized by any rational monoid
automaton over a finitely generated permutable monoid. We show that the class
of languages recognized by rational monoid automata over finitely generated
completely simple or completely 0-simple permutable monoids is a semi-linear
full trio. Furthermore, we investigate valence pushdown automata, and prove
that they are only as powerful as (finite) valence automata. We observe that
certain results proven for monoid automata can be easily lifted to the case of
context-free valence grammars.Comment: In Proceedings AFL 2017, arXiv:1708.0622
Sticker systems over monoids
Molecular computing has gained many interests among researchers since Head introduced the first theoretical model for DNA based computation using the splicing operation in 1987. Another model for DNA computing was proposed by using the sticker operation which Adlemanused in his successful experiment for the computation of Hamiltonian paths in a graph: a double stranded DNA sequence is composed by prolonging to the left and to the right a sequence of (single or double) symbols by using given single stranded strings or even more complex dominoes with sticky ends, gluing these ends together with the sticky ends of the current sequence according to a complementarity relation. According to this sticker operation, a language generative mechanism, called a sticker system, can be defined: a set of (incomplete) double-stranded sequences (axioms) and a set of pairs of single or double-stranded complementary sequences are given. The initial sequences are prolonged to the left and to the right by using sequences from the latter set, respectively. The iterations of these prolongations produce “computations” of possibly arbitrary length. These processes stop when a complete double stranded sequence is obtained. Sticker systems will generate only regular languages without restrictions. Additional restrictions can be imposed on the matching pairs of strands to obtain more powerful languages. Several types of sticker systems are shown to have the same power as regular grammars; one type is found to represent all linear languages whereas another one is proved to be able to represent any recursively enumerable language. The main aim of this research is to introduce and study sticker systems over monoids in which with each sticker operation, an element of a monoid is associated and a complete double stranded sequence is considered to be valid if the computation of the associated elements of the monoid produces the neutral element. Moreover, the sticker system over monoids is defined in this study
Graph Grammars, Insertion Lie Algebras, and Quantum Field Theory
Graph grammars extend the theory of formal languages in order to model
distributed parallelism in theoretical computer science. We show here that to
certain classes of context-free and context-sensitive graph grammars one can
associate a Lie algebra, whose structure is reminiscent of the insertion Lie
algebras of quantum field theory. We also show that the Feynman graphs of
quantum field theories are graph languages generated by a theory dependent
graph grammar.Comment: 19 pages, LaTeX, 3 jpeg figure
Computing downward closures for stacked counter automata
The downward closure of a language of words is the set of all (not
necessarily contiguous) subwords of members of . It is well known that the
downward closure of any language is regular. Although the downward closure
seems to be a promising abstraction, there are only few language classes for
which an automaton for the downward closure is known to be computable.
It is shown here that for stacked counter automata, the downward closure is
computable. Stacked counter automata are finite automata with a storage
mechanism obtained by \emph{adding blind counters} and \emph{building stacks}.
Hence, they generalize pushdown and blind counter automata.
The class of languages accepted by these automata are precisely those in the
hierarchy obtained from the context-free languages by alternating two closure
operators: imposing semilinear constraints and taking the algebraic extension.
The main tool for computing downward closures is the new concept of Parikh
annotations. As a second application of Parikh annotations, it is shown that
the hierarchy above is strict at every level.Comment: 34 pages, 1 figure; submitte
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