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:
“Two clergymen disputing whether ordination would be valid without the imposition of both hands, the more formal one said, “Do you think the Holy Dove could fly down with only one wing?””
—Horace Walpole (1717–1797)
“People in places many of us never heard of, whose names we can’t pronounce or even spell, are speaking up for themselves. They speak in languages we once classified as “exotic” but whose mastery is now essential for our diplomats and businessmen. But what they say is very much the same the world over. They want a decent standard of living. They want human dignity and a voice in their own futures. They want their children to grow up strong and healthy and free.”
—Hubert H. Humphrey (1911–1978)