Subsumption{oriented Push{down Automata ?

This paper presents Subsumption{oriented Push{Down Auto-mata (SPDA), a very general stack formalism used to describe forest (\AND{ OR" tree) traversals. These automata may be used for parsing or the interpretation of logic programs. SPDA allow a Dynamic Programming execution which breaks computations into combinable, sharable and storable sub{computations. They provide computation sharing and operational completeness and solves some of the problems posed by the usual depth{{rst, left{to{right traversals (as implemented in PROLOG). We give an axiom-atization of SPDA and two examples of their use: the evaluation of logic programs and parsing with Tree Adjoining Grammars. SPDA may also serve in other areas such as Constraint Logic Programming, Abstract Interpretations , or Contextual parsing.