2,780 research outputs found
Algorithmic properties of inverse monoids with hyperbolic and tree-like Sch\"utzenberger graphs
We prove that the class of finitely presented inverse monoids whose
Sch\"utzenberger graphs are quasi-isometric to trees has a uniformly solvable
word problem, furthermore, the languages of their Sch\"utzenberger automata are
context-free. On the other hand, we show that there is a finitely presented
inverse monoid with hyperbolic Sch\"utzenberger graphs and an unsolvable word
problem
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
A Fibrational Approach to Automata Theory
For predual categories C and D we establish isomorphisms between opfibrations
representing local varieties of languages in C, local pseudovarieties of
D-monoids, and finitely generated profinite D-monoids. The global sections of
these opfibrations are shown to correspond to varieties of languages in C,
pseudovarieties of D-monoids, and profinite equational theories of D-monoids,
respectively. As an application, we obtain a new proof of Eilenberg's variety
theorem along with several related results, covering varieties of languages and
their coalgebraic modifications, Straubing's C-varieties, fully invariant local
varieties, etc., within a single framework
Word problems recognisable by deterministic blind monoid automata
We consider blind, deterministic, finite automata equipped with a register
which stores an element of a given monoid, and which is modified by right
multiplication by monoid elements. We show that, for monoids M drawn from a
large class including groups, such an automaton accepts the word problem of a
group H if and only if H has a finite index subgroup which embeds in the group
of units of M. In the case that M is a group, this answers a question of Elston
and Ostheimer.Comment: 8 pages, fixed some typos and clarified ambiguity in the abstract,
results unchange
On the rational subset problem for groups
We use language theory to study the rational subset problem for groups and
monoids. We show that the decidability of this problem is preserved under graph
of groups constructions with finite edge groups. In particular, it passes
through free products amalgamated over finite subgroups and HNN extensions with
finite associated subgroups. We provide a simple proof of a result of
Grunschlag showing that the decidability of this problem is a virtual property.
We prove further that the problem is decidable for a direct product of a group
G with a monoid M if and only if membership is uniformly decidable for
G-automata subsets of M. It follows that a direct product of a free group with
any abelian group or commutative monoid has decidable rational subset
membership.Comment: 19 page
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