Advanced Lectures on Formal Languages and Automata Theory

Masahiko SAKAI Professor

Department: Graduate School of Information Science

Class Time: 2014 Spring Friday
Recommended for: Graduate School of Information Science Department of Computer Science and Mathematical Informatics students

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Course Aims

Automata theory is known as the basis of information science. For its application to compilers and model checking algorithms, it has become the theoretical foundation of all information processing. In this course, we will learn about the automaton on tree languages, and discuss its relationship with and application to logic.

Key Features

1. The course is mainly designed for students who studied automata theory during their undergraduate course, and hence designed understandable through comparison with that knowledge. In addition, I will try to give extra explanation for the benefit of students who do not have a deep knowledge of automata theory.

2. We will also study the relationship between automata theory and logic, and discuss the applications of tree automata theory on the field of logic.

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Hubert Common, et. al. Tree Automata Techniques and Applications, ( You can download the full text from this URL)

Course Requirements

Basic knowledge of automata is a prerequisite.

Related Resources

Reference about PLTL:

B.Hirsch, U.Hustadt: Translating PLTL into WS1S: Application Description, In Methods for Modalities II, University of Amsterdam, 2001 (

Course Schedule

Session Contents
1 Preliminary, NFTA
2 Equivalence between NFTA and DFTA, Pumping Lemma
3 Closure Properties
4 Myhill-Nerode Theorem
5 Regular Tree Grammar, Tree Regular Expressions I
6 Tree Regular Expressions II
7 Relations and NFTA
8 WSkS: Weak Second-Order Monadic Logic
9 Propositional Linear Time Logic
10 AWEDC: Automaton with Equality and Disequality Constraints
11 AWCBB: Automaton with Constraints Between Brothers, Reduction Automaton
12 Tree Transducers (1)
13 Tree Transducers (2)
14 Hedge Automaton
15 Summary / Final Exam


Grading will be based on reports (50%) and examination (50%).

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Lecture Handouts

Session 1
Basic notion, and NFTA (PDF, 132KB)
Session 2
Equivalence of NFTA and DFTA, and Pumping Lemma (PDF, 86KB)
Session 3
Closure (PDF, 30KB)
Session 4
Theorem of Myhill-Nerode (PDF, 90KB)
Session 5
Regular tree grammar, regular tree expression (PDF, 95KB)
Session 6
NFTA and regular expression (PDF, 84KB)
Session 7
Logic, automata and relations (PDF, 228KB)
Session 8
WSkS: Weakly Second-order monadic logic with k successors (PDF, 154KB)
Session 9
Propositional linear-time temporal logic (PDF, 82KB)
Session 10
AWEDC: NFTA with equality constraints (PDF, 133KB)
Session 11
AWCBB: NFTS with constraints between borthers, reduction automata (PDF, 29KB)
Session 12,13
Tree Transducers (PDF, 443KB)
Session 14
Hedge automaton (PDF, 124KB)

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Page last updated June 7, 2012

The class contents were most recently updated on the date indicated. Please be aware that there may be some changes between the most recent year and the current page.

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