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diff --git a/ata.mli b/ata.mli
index f5e2c4f..c56c22b 100644
--- a/ata.mli
+++ b/ata.mli
@@ -1,56 +1,71 @@
 type state = int
 val mk_state : unit -> state
 
-type predicate = Ptset.t*Ptset.t -> Tree.Binary.t ->  [ `True | `False | `Maybe ]
 type formula_expr =
     False
   | True
   | Or of formula * formula
   | And of formula * formula
-  | Atom of ([ `Left | `Right ] * bool * state * predicate option)
-and formula = { fid : int; pos : formula_expr; neg : formula; st : Ptset.t*Ptset.t;}
+  | Atom of ([ `Left | `Right | `LLeft | `RRight ] * bool * state)
+and formula = { fid : int; fkey : int; pos : formula_expr; neg : formula; st : (Ptset.t*Ptset.t*Ptset.t)*(Ptset.t*Ptset.t*Ptset.t); size: int;}
 val true_ : formula
 val false_ : formula
-val atom_ : ?pred:predicate option -> [`Left | `Right ] -> bool -> state -> formula
+val atom_ : [`Left | `Right | `LLeft | `RRight ] -> bool -> state -> formula
 val and_ : formula -> formula -> formula
 val or_ : formula -> formula -> formula
 val not_ : formula -> formula 
-val equal_form : formula -> formula -> bool
+(*val equal_form : formula -> formula -> bool *)
 val pr_frm : Format.formatter -> formula -> unit
 
 
-type property = [ `None | `Existential  ]
+module HTagSet : Hashtbl.S with type key = Ptset.t*Tag.t
 
-type t = {
+
+type 'a t = { 
   id : int;
-  states : Ptset.t;
+  mutable states : Ptset.t;
   init : Ptset.t;
-  final : Ptset.t;
+  mutable final : Ptset.t;
   universal : Ptset.t;
-  phi : (TagSet.t * state, bool * formula) Hashtbl.t;
-  delta : (TagSet.t, Ptset.t * bool * Ptset.t * Ptset.t) Hashtbl.t;
-  properties : (state,property) Hashtbl.t;
+  starstate : Ptset.t option;
+  (* Transitions of the Alternating automaton *)
+  phi : (state,(TagSet.t*(bool*formula*bool)) list) Hashtbl.t;
+  sigma : (int,('a t -> Tree.t -> Tree.t -> Ptset.t*'a)) Hashtbl.t;
 }
-val dump : Format.formatter -> t -> unit
+
+val dump : Format.formatter -> 'a t -> unit
     
 module Transitions : sig
-type t = state*TagSet.t*bool*formula
+type t = state*TagSet.t*bool*formula*bool
 (* Doing this avoid the parenthesis *)
 val ( ?< ) : state -> state 
-val ( >< ) : state -> TagSet.t*bool -> state*(TagSet.t*bool)
-val ( >=> ) : state*(TagSet.t*bool) -> formula -> t
+val ( >< ) : state -> TagSet.t*bool -> state*(TagSet.t*bool*bool)
+val ( ><@ ) : state -> TagSet.t*bool -> state*(TagSet.t*bool*bool)
+val ( >=> ) : state*(TagSet.t*bool*bool) -> formula -> t
 val ( +| ) : formula -> formula -> formula
 val ( *& ) : formula -> formula -> formula
-val ( ** ) : [`Left | `Right ] -> state -> formula
+val ( ** ) : [`Left | `Right | `LLeft | `RRight ] -> state -> formula
 
 end
 type transition = Transitions.t
-val equal_trans : transition -> transition -> bool
+val equal_trans : transition -> transition -> bool 
 
 
-module BottomUpNew : 
-sig
-  val miss : int ref
-  val call : int ref
-  val run : t -> Tree.Binary.t -> Tree.Binary.t list
-end
+  module type ResultSet = 
+  sig
+    type t
+    val empty : t
+    val cons : Tree.t -> t -> t
+    val concat : t -> t -> t
+    val iter : (Tree.t -> unit) -> t -> unit
+    val fold : (Tree.t -> 'a -> 'a) -> t -> 'a -> 'a
+    val map : (Tree.t -> Tree.t) -> t -> t
+    val length : t -> int
+  end
+
+  module IdSet : ResultSet
+
+  val top_down_count : 'a t -> Tree.t -> int
+  val top_down : 'a t -> Tree.t -> IdSet.t
+  val bottom_up_count_contains : 'a t -> Tree.t -> int
+  val bottom_up_count : 'a t -> Tree.t -> Tag.t -> int