Easy multiplications. I. The realm of Kleene's theorem
Information and Computation
Sequential grammars and automata with valances
Theoretical Computer Science
The Accepting Power of Finite Automata over Groups
New Trends in Formal Languages - Control, Cooperation, and Combinatorics (to Jürgen Dassow on the occasion of his 50th birthday)
On groups whose word problem is solved by a counter automaton
Theoretical Computer Science
Word problems recognisable by deterministic blind monoid automata
Theoretical Computer Science
Rational subsets of polycyclic monoids and valence automata
Information and Computation
On the capabilities of grammars, automata, and transducers controlled by monoids
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
| Hi-index | 5.23 |
We consider a natural extension of the usual definition of M-automata (also known as extended automata or valence automata) which permits the automaton to utilise more of the structure of each monoid, and additionally allows us to define S-automata for S an arbitrary semigroup. In the monoid case, the resulting automata are equivalent to the valence automata with rational target sets which arise in the theory of regulated rewriting systems. We study these automata in the case where the register semigroup is completely simple or completely 0-simple, obtaining a complete characterisation of the classes of languages corresponding to such semigroups, in terms of their maximal subgroups. In the process, we obtain a number of results about rational subsets of Rees matrix semigroups which are likely to be of independent interest.