Mikołaj Bojańczyk

Przekształcenia automatowe 2026 • Transducers


This is a course on transducers, whose previous edition is here.

Grade. Your grade is the weighted average 2/3 * (grade from oral exam)  + 1/3 * (grade from homework). There will be 3 groups of homework problems.

Lecture notes. Here are versions of the lecture notes:

 

Exam

There are 13 topics for the exam : 1 Mealy, 4 Rational, 6 Regular and 2 Polyregular. These are listed below, together with the section numbers in the notes.

Mealy machines

  1. (A.1 and A.2) Definition of  Mealy machines and the Krohn-Rhodes theorem

Rational functions

  1. (B.1) Definition of rational relations, and undecidability of their equivalence problem.
  2. (B.2) Rational functions,  their equivalence with bimachines, and the decomposition of rational functions into primes.
  3. (B.3) Equivalence is decidable for rational functions
  4. (B.4) Machine independent characterizations of Mealy machines, sequential functions,  subsequential functions and rational functions

Regular functions

  1. (C.1) The prime regular functions and their continuity
  2. (C.2.1) Continuity of two-way transducers
  3. (C.2.2) Closure under composition for two-way transducers
  4. (C.2.3) Decomposition of two-way transducers into primes
  5. (C.3) SST’s and their equivalence two two-way transducers
  6. (C.4.3) Regular functions in terms of logic

Polyregular functions

  1. (D.1) For-transducers and their equialence with prime polyregular functions
  2. (D.2) Pebble transducers and their equivalence to for-transducers