Comparisons between Measures of Nondeterminism on Finite Automata

We study the interrelationships between various measures of nondeterminism for finite automata. The tree width of an NFA (nondeterministic finite automaton) A is a function that associates a positive integer n to the maximum number of leaves in any computation tree of A on an input of length n. The trace of an NFA is defined in terms of the maximum product of the degrees of nondeterministic choices in computation on inputs of given length. We establish upper and lower bounds for the trace function of an NFA in terms of its tree width. Additionally, the unbounded trace of an NFA has exponential growth.

[1]  Jonathan Goldstine,et al.  On Measuring Nondeterminism in Regular Languages , 1990, Inf. Comput..

[2]  Martin Kutrib,et al.  Descriptional Complexity of (Un)ambiguous Finite State Machines and Pushdown Automata , 2010, RP.

[3]  Hing Leung.  Separating Exponentially Ambiguous Finite Automata from Polynomially Ambiguous Finite Automata , 1998, SIAM J. Comput..

[4]  Hartmut Klauck,et al.  Measures of Nondeterminism in Finite Automata , 2000, ICALP.

[5]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[6]  Oscar H. Ibarra,et al.  Relating the Type of Ambiguity of Finite Automata to the Succinctness of Their Representation , 1989, SIAM J. Comput..

[7]  Jeffrey Shallit,et al.  A Second Course in Formal Languages and Automata Theory , 2008 .

[8]  Hing Leung.  Descriptional complexity of nfa of different ambiguity , 2005, Int. J. Found. Comput. Sci..

[9]  Selim G. Akl,et al.  State Complexity and Limited Nondeterminism , 2012, DCFS.

[10]  Alexander Okhotin.  Unambiguous finite automata over a unary alphabet , 2012, Inf. Comput..

[11]  Hartmut Klauck,et al.  Communication Complexity Method for Measuring Nondeterminism in Finite Automata , 2002, Inf. Comput..

[12]  Andreas Malcher,et al.  Descriptional Complexity of Machines with Limited Resources , 2002, J. Univers. Comput. Sci..

[13]  Hing Leung.  On finite automata with limited nondeterminism , 1998, Acta Informatica.

[14]  Detlef Wotschke,et al.  Amounts of nondeterminism in finite automata , 1980, Acta Informatica.

[15]  Jonathan Goldstine,et al.  On the Relation between Ambiguity and Nondeterminism in Finite Automata , 1992, Inf. Comput..

[16]  Martin Kutrib,et al.  Descriptional and computational complexity of finite automata - A survey , 2011, Inf. Comput..