On the Expressive Power of FO[ + ]

The characterization of the class of FO[+]-definable languages by some generating or recognizing device is still an open problem. We prove that, restricted to bounded languages, this class coincides with the class of semilinear languages. We also study some closure properties of FO[+]-definable languages which, as a by-product, allow us to give an alternative proof that the Dyck languages cannot be defined in FO[+].

[1]  Michael Sipser,et al.  Parity, circuits, and the polynomial-time hierarchy , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[2]  Walter L. Ruzzo.  On Uniform Circuit Complexity , 1981, J. Comput. Syst. Sci..

[3]  D. H. Robinson,et al.  Parallel algorithms for group word problems , 1993 .

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

[5]  Michael A. Harrison,et al.  Introduction to formal language theory , 1978 .

[6]  S. Ginsburg,et al.  BOUNDED ALGOL-LIKE LANGUAGES^) , 1964 .

[7]  Noam Chomsky,et al.  The Algebraic Theory of Context-Free Languages* , 1963 .

[8]  J. Shepherdson,et al.  Computer programming and formal systems , 1965 .

[9]  Neil Immerman,et al.  First-order expressibility of languages with neutral letters or: The Crane Beach conjecture , 2005, J. Comput. Syst. Sci..

[10]  György E. Révész.  Introduction to formal languages , 1983 .

[11]  Ingo Wegener,et al.  The complexity of Boolean functions , 1987 .

[12]  Tao Jiang,et al.  Some Subclasses of Context-Free Languages In NC1 , 1988, Inf. Process. Lett..

[13]  Howard Straubing.  Finite Automata, Formal Logic, and Circuit Complexity , 1994, Progress in Theoretical Computer Science.

[14]  James C. Corbett,et al.  On the Relative Complexity of Some Languages in NC , 1989, Inf. Process. Lett..

[15]  Oscar H. Ibarra,et al.  Simple Matrix Languages , 1970, Inf. Control..

[16]  S. Ginsburg,et al.  Bounded -like languages , 1964 .

[17]  Seymour Ginsburg,et al.  The mathematical theory of context free languages , 1966 .

[18]  Oscar H. Ibarra,et al.  A Note on Semilinear Sets and Bounded-Reversal Multihead Pushdown Automata , 1974, Inf. Process. Lett..

[19]  Dominique Perrin,et al.  Finite Automata , 1958, Philosophy.