BEGIN:VCALENDAR VERSION:2.0 PRODID:ILLC Website X-WR-TIMEZONE:Europe/Amsterdam BEGIN:VTIMEZONE TZID:Europe/Amsterdam X-LIC-LOCATION:Europe/Amsterdam BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19700329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19701025T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:/NewsandEvents/Archives/2018/newsitem/9891/19- April-2018-ILLC-Seminar-Daniela-Petrisan DTSTAMP:20190307T164600 SUMMARY:ILLC Seminar, Daniela Petrisan ATTENDEE;ROLE=Speaker:Daniela Petrisan DTSTART;TZID=Europe/Amsterdam:20180419T100000 DTEND;TZID=Europe/Amsterdam:20180419T105000 LOCATION:ILLC Seminar Room F1.15, Science Park 107 , Amsterdam 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.
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\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.
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\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/Archives/2018/newsitem/9891/19- April-2018-ILLC-Seminar-Daniela-Petrisan CONTACT:Yde Venema at Y.Venema at uva.nl END:VEVENT END:VCALENDAR