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BEGIN:VEVENT
UID:/NewsandEvents/Events/Upcoming-Events/newsitem
/9891/19-April-2018-ILLC-Seminar-Daniela-Petrisan
DTSTAMP:20180418T125006
SUMMARY:ILLC Seminar, Daniela Petrisan
ATTENDEE;ROLE=Speaker:Daniela Petrisan
DTSTART:20180419T100000
DTEND:20180419T105000
LOCATION:ILLC Seminar Room F1.15, Science Park 107
, The Netherlands
DESCRIPTION:In this talk I will present an overvie
w of some recent results involving applications of
duality and category theory in automata and langu
age theory. One such strand of research involves
a generic approach to automata minimization. We
depart from the standard coalgebraic approach and
model automata as functors from a category specify
ing the input of the machine to another category w
hich captures the structure of it's output. We ide
ntify sufficient conditions on the output category
which ensure the existence of minimal automata. T
his allows us to cover awide range of examples by
systematically applying the same category-theoreti
c principles in various instances. A second rese
arch axis heavily uses duality theory to extend al
gebraic methods from the theory of regular languag
es to the non-regular setting. There are a plethor
a of results relating algebraic and logical charac
terizations of classes of regular languages. We ai
m to develop the tools that allow us to obtain suc
h correspondences forclasses of non-regular langua
ges. I will explain in detail how thesyntactic mon
oid of a language can be seen as the dual of the B
ooleanalgebra spanned by the quotients of that lan
guage. This paves the way for defining a suitable
notion of recognisers for non-regular languages an
d to extend in this setting standard constructions
from monoids that are the algebraic counterpart o
f logical quantifiers.
X-ALT-DESC;FMTTYPE=text/html:\n In this talk I
will present an overview of some recent results i
nvolving applications of duality and category theo
ry in automata and language theory.

\n

\n
One such strand of research involves a generic ap
proach to automata minimization. We depart f
rom the standard coalgebraic approach and model au
tomata as functors from a category specifying the
input of the machine to another category which cap
tures the structure of it's output. We identify su
fficient conditions on the output category which e
nsure the existence of minimal automata. This allo
ws us to cover awide range of examples by systemat
ically applying the same category-theoretic princi
ples in various instances.

\n

\n A second
research axis heavily uses duality theory to exte
nd algebraic methods from the theory of regular la
nguages to the non-regular setting. There are a pl
ethora of results relating algebraic and logical c
haracterizations of classes of regular languages.
We aim to develop the tools that allow us to obtai
n such correspondences forclasses of non-regular l
anguages. I will explain in detail how thesyntacti
c monoid of a language can be seen as the dual of
the Booleanalgebra spanned by the quotients of tha
t language. This paves the way for defining a suit
able notion of recognisers for non-regular languag
es and to extend in this setting standard construc
tions from monoids that are the algebraic counterp
art of logical quantifiers.

\n
URL:/NewsandEvents/Events/Upcoming-Events/newsitem
/9891/19-April-2018-ILLC-Seminar-Daniela-Petrisan
CONTACT:Yde Venema at Y.Venema at uva.nl
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