Logic and Branching Automata

The first result presented in this paper is the closure under complementation of the class of languages of finite N-free posets recognized by branching automata. Relying on this, we propose a logic, named Presburger-MSO or P-MSO for short, precisely as expressive as branching automata. The P-MSO theory of the class of all finite N-free posets is decidable.

[1]  Tayssir Touili,et al.  On Computing Reachability Sets of Process Rewrite Systems , 2005, RTA.

[2]  Zoltán Ésik,et al.  Automata on Series-Parallel Biposets , 2001 .

[3]  Pascal Weil,et al.  Rationality in Algebras with a Series Operation , 2002, Inf. Comput..

[4]  S. Ginsburg,et al.  Semigroups, Presburger formulas, and languages. , 1966 .

[5]  M. Schützenberger,et al.  Rational sets in commutative monoids , 1969 .

[6]  Eugene L. Lawler,et al.  The Recognition of Series Parallel Digraphs , 1982, SIAM J. Comput..

[7]  Silvano Dal-Zilio,et al.  XML Schema, Tree Logic and Sheaves Automata , 2003, RTA.

[8]  Hendrik Jan Hoogeboom,et al.  Text Languages in an Algebraic Framework , 1996, Fundam. Informaticae.

[9]  Wolfgang Thomas,et al.  Languages, Automata, and Logic , 1997, Handbook of Formal Languages.

[10]  Paulien ten Pas,et al.  Monadic second-order definable text languages , 1997, Theory of Computing Systems.

[11]  C. C. Elgot.  Decision problems of finite automata design and related arithmetics , 1961 .

[12]  Pascal Weil,et al.  Series-parallel languages and the bounded-width property , 2000, Theor. Comput. Sci..

[13]  Dietrich Kuske,et al.  Infinite Series-Parallel Posets: Logic and Languages , 2000, ICALP.

[14]  Pascal Weil,et al.  Series-Parallel Posets: Algebra, Automata and Languages , 1998, STACS.

[15]  J. Büchi.  Weak Second‐Order Arithmetic and Finite Automata , 1960 .

[16]  Jacobo Valdes.  Parsing Flowcharts and Series-Parallel Graphs , 1978 .

[17]  S C Kleene,et al.  Representation of Events in Nerve Nets and Finite Automata , 1951 .

[18]  Pascal Weil,et al.  A Kleene Iteration for Parallelism , 1998, FSTTCS.

[19]  Thomas Schwentick,et al.  Counting in trees , 2008, Logic and Automata.