Formal Languages
Real world tasks are formalized by programming languages, which are executed on computers based on the von Neumann architecture. Since programming languages are only comfortable representations of the Turing machine any program on a von Neumann computer has the same properties and limitations as the Turing machine or its equivalent representation. Consequently every programming language such as CPU level machine code, assembler, or any high level programming language has the same expressional power as the underlying Turing machine is able to compute. There is no semantic gap between them since a program is transferred from the high level language to the machine code by a program, e.g. a compiler which itself runs on a Turing machine without any user interaction. The semantic gap actually opens between the selection of the rules and the representation of the task.
Read more about this topic: Semantic Gap
Famous quotes containing the words formal and/or languages:
“This is no argument against teaching manners to the young. On the contrary, it is a fine old tradition that ought to be resurrected from its current mothballs and put to work...In fact, children are much more comfortable when they know the guide rules for handling the social amenities. Its no more fun for a child to be introduced to a strange adult and have no idea what to say or do than it is for a grownup to go to a formal dinner and have no idea what fork to use.”
—Leontine Young (20th century)
“The less sophisticated of my forbears avoided foreigners at all costs, for the very good reason that, in their circles, speaking in tongues was commonly a prelude to snake handling. The more tolerant among us regarded foreign languages as a kind of speech impediment that could be overcome by willpower.”
—Barbara Ehrenreich (b. 1941)