Need for Reachability

Weak Monadic Logic of One Successor

We use the basic results of automata and formal languages to decide the formulas of interest.

Strings and languages

Finite state machine

Determinization of finite state machine

Finite state machine with epsilon transitions

Closure properties of finite state machines

Regular expression

Equivalence of finite state machine and regular expression languages

Automata and languages:

• Introduction to the Theory of Computation
• Introduction to Automata Theory, Languages, and Computation

Regular expressions for automata with parallel inputs

Using automata to decide Presburger arithmetic

More:

• LASH Toolset
• LIRA: Handling Constraints of Linear Arithmetics over the Integers and the Reals

Weak Monadic Logic of One Successor

Using Automata to Decide WS1S

Remarks on WS1S Complexity

Expressing finite automata in MSOL over strings

Encoding lists using MSOL over strings

Tree automata

More:

• Languages, Automata, and Logic, by Wolfgang Thomas
• Tree Automata Techniques and Applications (Tata book)
• The MONA Project
• Timbook for Reachability Analysis and Tree Automata Calculations
• Decidability of Second-Order Theories and Automata on Infinite Trees
• Efficient Static Analysis of XML Paths and Types