Regular cost functions and stabilization monoids
14/03/2016 14  15  16  17 Março, sala 6.2.33  DM  FCUL
Thomas Colcombet (LIAFA, Université Paris Diderot)
Departamento de Matemática  FCUL
Regular cost functions form a quantitative extension to the classical notion of regular languages.
However, contrary to other models, it focuses only on boundedness questions. Hence, cost
functions are maps from words to ?∪∞, which are considered modulo ‘preservation of bounds’. The
resulting theory resembles a lot the one for regular languages. In particular, many models of
acceptors are effectively equivalent: logic (cost monadic secondorder logic), automata (Bautomata/
Sautomata), expressions (Brational expression/Srational expressions), and algebra
(stabilisation monoids).
In this course, we will introduce some of these objects, present the central results and the
remaining open problem. We will be paying a particular attention to the algebraic formalism of
stabilisaiton monoids. Stabilisation monoids are ordered monoids enriched with a map from
idempotents to idempotents which essentially represents the effect of iterating a large (unbounded)
number of times the element. We will see how associating semantics to these objects. We will also
show how these can be used in ‘la Schützenberger’ algebraic characterization results yielding
important decidable subclasses.
14^{ } March  15:30 – 17:30
15  March  9:30 – 11:30
16  March  16:00 – 18:00
17  March  10:30 – 12:30
