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Dynamic Turing Machine: model and properties for runtime code changes

Rudy J.

Computer Science

2016

Vol. 17 (2)

187--224

In this paper, a dynamic model of computation based on the Universal Turing Machine is proposed. This model is capable of applying runtime code modifications for 3-symbol deterministic Turing Machines at runtime and requires a decomposition of the simulated machine into parts called subtasks. The algorithm for performing runtime changes is considered, and the ability to apply runtime changes is studied through computer simulations. Theoretical properties of the proposed model, including computational power as well as time and space complexity, are studied and proven. Connections between the proposed model and Oracle Machines are discussed. Moreover, a possible method of implementation in real-life systems is proposed.

Turing machine approach to runtime software adaptation

Rudy J.

Computer Science

2014

Vol. 15 (3)

293--310

In this paper, the problem of applying changes to software at runtime is considered. The computability theory is used in order to develop a more general and programming-language-independent model of computation with support for runtime changes. Various types of runtime changes were defined in terms of computable functions and Turing machines. The properties of such functions and machines were used to prove that arbitrary runtime changes on Turing machines are impossible in general cases. A method of Turing machine decomposition into subtasks was presented and runtime changes were defined through transformations of the subtask graph. Requirements for the possible changes were considered with regard to the possibility of subtask execution during such changes. Finally, a runtime change model of computation was defined by extension of the Universal Turing Machine.

Variable Complexity of Simple Programs

Holzer M., Kutrib M.

Fundamenta Informaticae

2006

Vol. 74, nr 4

511-528

The number of registers or variables of a LOOP-, WHILE-, or GOTO-program, needed to compute a certain (partial) function from non-negative integers into non-negative integers, is a natural measure of complexity. We show that the hierarchy of LOOP-computable (WHILE-, and GOTO-computable, respectively) functions f:\mathbbNŽ \mathbbN (partial functions f:\mathbbN\hookrightarrow \mathbbN, respectively) which is induced by the number of registers collapses to level four (three, respectively). So, there exist universal WHILE- and GOTO-programs with a constant number of registers. In all three cases we give a characterization of the functions that can be computed by one register only. These characterizations are used to show that the first levels of the register hierarchies are strict, and to compare these levels. Surprisingly, for total functions it turns out that the bottom level of the LOOP-hierarchy is incomparable (with respect to set inclusion) to the bottom levels of the WHILE- and GOTO-hierarchies. Finally we briefly discuss the impact of the register operations on the presented results.