/pdf/the-calculi-of-emergence-computation-dynamics-and-induction-46gxa5cp8v.pdf

The calculi of emergence: computation, dynamics and induction

Quantum automata and quantum grammars

To study quantum computation, it might be helpful to generalize structures from language and automata theory to the quantum case. To that end, we propose quantum versions of finite-state and push-down automata, and regular and context-free grammars. We find analogs of several classical theorems, including pumping lemmas, closure properties, rational and algebraic generating functions, and Greibach normal form. We also show that there are quantum context-free languages that are not context-free.

Quantum Automata and Quantum Grammars

: This project was concerned with the development of correct and reusable software through the use of higher order abstractions (function, control, assignment, process) and reflection. A semantic framework for these notions will be the basis of an experimental system for manipulating and reasoning about programs. The goals of this project were the development of logical formalisms for reasoning about programs that use abstractions and reflection, and the application of these theoretical results to selected software problems. Example applications include (1) clarification of existing programming paradigms, (2) analysis of existing and proposed languages used in the DARPA community for specifying, writing, and transforming programs, and (3) development and implementation of tools for computer aided reasoning about and operating on programs. The accomplishments of this project fit into four categories: (1) logics for reasoning about function and control abstractions; (2) logics for reasoning about data mutation; (3) logics for reasoning about function and control abstractions in the presence of mutable data; and (4) applying methodology for reasoning about programs to the mechanical verification of hardware.

Mathematical Theory of Computation

A new class of languages, called multi-push-down (mpd), that generalize the classical context-free (cf, or Chomsky type 2) ones is introduced. These languages preserve some important properties of ...

Multi-push-down languages and grammars

QRT FIFO automata, breadth-first grammars and their relations

Chains (or cascade composition) of push-down transducers are introduced as a model of multi-pass compilers. We focus on deterministic chains, since nondeterministic transducer chains of length two define the recursively enumerable sets. Deterministic chains recognize in linear time a superset of context-free deterministic languages. This family is $\mathcal{CH}$ closed under Boolean operations, disjoint shuffle,and reverse deterministic pushdown translation, but not under homomorphism. Equivalent definitions of the family in terms of composition of syntax-directed translation schemes and control languages are considered. The family is a strict hierarchy ordered by the length of the chain. The complexity of $\mathcal{CH}$ is obviously linear, but not all linear-time parsable languages are in $\mathcal{CH}$. On the other hand it strictly includes the Boolean closure of deterministic languages. Finally $\mathcal{CH}$ is not comparable with another classical Boolean algebra of formal languages, namely real-ti...

On deterministic multi pass analysis

We describe firstly an unilateral problem for the homogeneous wave equation in two variables, giving existence, uniqueness and continuous dependence results, and a description of the pencil of the solutions in the cases where uniqueness fails to hold. In particular we prove the existence of super- and subsolutions. We apply then the above results to the equation ytt−yxx=F(x,t,y) with unilateral constraints whose support lies on a line in a generalized half strip in the (x,t) plane.

Discontinuous solutions of a nonlinear hyperbolic equation with unilateral constraints

We introduce BD (Breadth-Depth) grammars which extend context-free grammars by allowing breadth-first derivations. Their languages are recognized by Deque (double ended queue) automata having a sin...

Claudio Citrini

Papers

Multi-push-down languages and grammars

QRT FIFO automata, breadth-first grammars and their relations

On deterministic multi pass analysis

Discontinuous solutions of a nonlinear hyperbolic equation with unilateral constraints

Breadth and depth grammars and deque automata