module TS : sig
  type t
  val empty : t
  val cons : Tree.t -> t -> t
  val append : Tree.t -> t -> t
  val concat : t -> t -> t
  val length  : t -> int
  val iter : (Tree.t -> unit) -> t -> unit
end

type state = int
val mk_state : unit -> state

type formula_expr =
    False
  | True
  | Or of formula * formula
  | And of formula * formula
  | 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_ : [`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 pr_frm : Format.formatter -> formula -> unit


module HTagSet : Hashtbl.S with type key = Ptset.t*Tag.t

type dispatch = { first : Tree.t -> Tree.t;
		  flabel : string;
		  next : Tree.t -> Tree.t -> Tree.t;	
		  nlabel : string;
		}
type t = { 
    id : int;
    mutable states : Ptset.t;
    init : Ptset.t;
    mutable final : Ptset.t;
    universal : Ptset.t;
    (* Transitions of the Alternating automaton *)
    phi : (state,(TagSet.t*(bool*formula*bool)) list) Hashtbl.t;
    sigma : (dispatch*bool*formula) HTagSet.t;
}
val dump : Format.formatter -> t -> unit
    
module Transitions : sig
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*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 | `LLeft | `RRight ] -> state -> formula

end
type transition = Transitions.t
val equal_trans : transition -> transition -> bool 



(*module BottomUpJumpNew : 
sig *)
  val run : t -> Tree.t -> TS.t*int
  val run_count : t -> Tree.t -> int
  val run_time :  t -> Tree.t -> TS.t*int
(*end *)