31 research outputs found
Evolving MultiAlgebras unify all usual sequential computation models
It is well-known that Abstract State Machines (ASMs) can simulate
"step-by-step" any type of machines (Turing machines, RAMs, etc.). We aim to
overcome two facts: 1) simulation is not identification, 2) the ASMs simulating
machines of some type do not constitute a natural class among all ASMs. We
modify Gurevich's notion of ASM to that of EMA ("Evolving MultiAlgebra") by
replacing the program (which is a syntactic object) by a semantic object: a
functional which has to be very simply definable over the static part of the
ASM. We prove that very natural classes of EMAs correspond via "literal
identifications" to slight extensions of the usual machine models and also to
grammar models. Though we modify these models, we keep their computation
approach: only some contingencies are modified. Thus, EMAs appear as the
mathematical model unifying all kinds of sequential computation paradigms.Comment: 12 pages, Symposium on Theoretical Aspects of Computer Scienc
Extending the Loop Language with Higher-Order Procedural Variables
Technical Report of the LACLWe extend Meyer and Ritchie's Loop language with higher-order procedures and procedural variables and we show that the resulting programming language (called Loopω) is a natural imperative counterpart of Gödel System T. The argument is two-fold: 1. we define a translation of the Loopω language into System T and we prove that this translation actually provides a lock-step simulation, 2. using a converse translation, we show that Loopω is expressive enough to encode any term of System T. Moreover, we define the “iteration rank” of a Loopω program, which corresponds to the classical notion of “recursion rank” in System T, and we show that both trans- lations preserve ranks. Two applications of these results in the area of implicit complexity are described