Automated Induction with Constrained Tree Automata

A high capacity blender has been devised which is adaptable for use in achieving the proper blend of liquid-to-liquid or liquid-to-solid constituents making up a gel composition for use in fracturing oil and gas well formations in which a high speed impeller is mounted for rotation concentrically within an outer casing and has a solids inlet which is isolated from the liquid inlet. A series of liquid inlet apertures are disposed in outer concentric surrounding relation to the impeller, and impeller vanes within the impellers are operative to impart a centrifugal force to solids introduced therein whereby to direct the solids and materials radially and outwardly under considerable force into the liquid stream which is directed axially along the inner wall of a mixing chamber. A preselected amount of the blended materials may be recirculated through the impeller inlet, and varying amounts of the solids in proportion to the liquid may be introduced through the impeller region while assuring intimate mixing with the liquid stream in a single stage for introduction under the desired pressure for pumping into the well.

[1]  Hubert Comon Unification et disunification : théorie et applications , 1988 .

[2]  Deepak Kapur,et al.  Constructors can be Partial too , 1997 .

[3]  Hubert Comon-Lundh,et al.  Unification et disunification : théorie et applications , 1988 .

[4]  Michaël Rusinowitch,et al.  Implicit induction in conditional theories , 2004, Journal of Automated Reasoning.

[5]  Jean-Pierre Jouannaud,et al.  Rewrite Systems , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[6]  Alan Robinson,et al.  The Inverse Method , 2001, Handbook of Automated Reasoning.

[7]  Florent Jacquemard,et al.  Ground reducibility is EXPTIME-complete , 2003, Inf. Comput..

[8]  José Meseguer,et al.  Specification and proof in membership equational logic , 2000, Theor. Comput. Sci..

[9]  A. Bouhoula,et al.  Verifying Regular Trace Properties of Security Protocols with Explicit Destructors and Implicit Induction , 2007 .

[10]  Jared Davis Finite Set Theory based on Fully Ordered Lists , 2004, ACL 2004.

[11]  Hubert Comon,et al.  Tree automata techniques and applications , 1997 .

[12]  Michaël Rusinowitch,et al.  Tree automata with equality constraints modulo equational theories , 2006, J. Log. Algebraic Methods Program..

[13]  Sorin Stratulat,et al.  A General Framework to Build Contextual Cover Set Induction Provers , 2001, J. Symb. Comput..

[14]  Ian Stark,et al.  Free-Algebra Models for the pi-Calculus , 2005, FoSSaCS.

[15]  C. Kirchner,et al.  Deduction with symbolic constraints , 1990 .

[16]  Jean-Pierre Jouannaud,et al.  Automata-Driven Automated Induction , 2001, Inf. Comput..

[17]  Adel Bouhoula,et al.  Automated Theorem Proving by Test Set Induction , 1997, J. Symb. Comput..

[18]  Jan van Leeuwen,et al.  Handbook of Theoretical Computer Science, Vol. B: Formal Models and Semantics , 1994 .

[19]  Florent Jacquemard,et al.  Tree Automata with Memory, Visibility and Structural Constraints , 2007, FoSSaCS.

[20]  Hantao Zhang,et al.  Implementing Contextual Rewriting , 1992, CTRS.