论文信息 - p329 The µ-calculus alternation-depth hierarchy is strict on binary trees

p329 The µ-calculus alternation-depth hierarchy is strict on binary trees

Nous donnons dans cet article une preuve simple que la hierarchie d'alternance de points fixes pour le μ-calcul sur les arbres binaires est infinie. Les temoins en sont les automates qui determinent l'existence d'une strategie gagnante pour le jeu de parite joue sur un arbre binaire.

André Arnold | A. Arnold

[1] Yuri Gurevich,et al. Trees, automata, and games , 1982, STOC '82.

[2] Wolfgang Thomas,et al. A hierarchy of sets of infinite trees , 1983 .

[3] Damian Niwinski. On Fixed-Point Clones (Extended Abstract) , 1986, ICALP.

[4] E. Muller David,et al. Alternating automata on infinite trees , 1987 .

[5] André Arnold. Logical Definability of Fixed Points , 1988, Theor. Comput. Sci..

[6] Andrzej Wlodzimierz Mostowski. Hierarchies of Weak Automata and Weak Monadic Formulas , 1991, Theor. Comput. Sci..

[7] E. Allen Emerson,et al. Tree automata, mu-calculus and determinacy , 1991, [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science.

[8] David E. Muller,et al. Alternating Automata, the Weak Monadic Theory of Trees and its Complexity , 1992, Theor. Comput. Sci..

[9] Damian Niwinski,et al. Fixed point characterization of weak monadic logic definable sets of trees , 1992, Tree Automata and Languages.

[10] Giacomo Lenzi. A Hierarchy Theorem for the µ-Calculus , 1996, ICALP.

[11] Julian Bradfield. CONCUR '96: Concurrency Theory , 1996 .

[12] Damian Niwinski,et al. Fixed Point Characterization of Infinite Behavior of Finite-State Systems , 1997, Theor. Comput. Sci..

[13] Julian C. Bradfield,et al. Fixpoint Alternation: Arithmetic, Transition Systems, and the Binary Tree , 1998 .

[14] Julian C. Bradfield. Simplifying the Modal Mu-Calculus Alternation Hierarchy , 1998, STACS.