Showing papers on "Formal language published in 1968"
372 citations
TL;DR: A general set of conditions is given under which a property is undecidable for a family of languages.
Abstract: A general set of conditions is given under which a property is undecidable for a family of languages. Examples are given of the application of this result to wellknown families of languages.
76 citations
TL;DR: In this article, the principal methods of describing languages and the principal results concerning each method are given.
Abstract: Let ~ be a finite set of symbols, or alphabet. Define ~* to be the set of all finite length strings of symbols in X, including ~, the string of length 0. A language is a subset of X*, for some alphabet ~. Clearly, the natural languages and programming languages are languages in the formal sense. The theory of languages is concerned with the description of languages, their recognition and processing. A language may contain an infinite number of strings, so at the least, one needs a finite description of the language. Particular types of finite descriptions will yield useful properties of the languages they define, especially when the class of languages they define is "small" (i.e., not every language of conceivable interest is described). If C is the class of languages defined by a certain type of description, one would like to know whether membership in C is preserved under various operations. One would like to know that the languages in class C could be recognized quickly and simply, especially if one were attempting to develop a compiling system for a language or languages in C. Also useful are characterizations of languages in C, so one can tell easily if a given language is in class C. Finally, one wants algorithms, if they exist, to answer certain questions about the languages in C, such as: "Is string w in language L?" In this article, we will give the principal methods of describing languages and the principal results concerning each method.
42 citations
15 Oct 1968
TL;DR: It is shown that a set of regular expressions can be used to characterize every language which is generated by a non-expansive context-free grammar, i.e. which is a standard matching-choice set as defined by Yntema.
Abstract: In this paper we study some classes of irregular languages which can be denoted by regularlike expressions It is shown that a set of regular expressions can be used to characterize every language which is generated by a non-expansive context-free grammar, ie which is a standard matching-choice set as defined by Yntema Characterizations are given for the linear, metalinear and ultralinear languages Some known results are presented in a simpler and more intuitive fashion by using the notion of a finite automaton with a folded tape It is next shown that the model used can be naturally extended to a subfamily of contextsensitive languages
25 citations
DOI•
01 Jul 1968
TL;DR: The Formal Methods course is about formally writing down languages (for example programming languages) and introduces these definitions: Rule: Finite set of premises and a conclusion.
Abstract: The Formal Methods course is about formally writing down languages (for example programming languages). Formal languages are understandable by a computer. A formal language consists of syntax and semantics. The syntax describes elements of a language , whereas the semantics describes the meaning. For example: Syntax Semantics objects Michael (the person) 13 XIII 1101 13 (all three mean the same thing) facts Michael is a student at IST true functions circuit programs dynamic systems automata programs We give now an example of a language defining a system: 1.1 Language of binary numbers 0 1 x x0 x x1 The expression above the rule is called a premise, the expression below the rule a conclusion. We introduce these definitions: Rule: Finite set of premises and a conclusion 1
14 citations
15 Oct 1968
TL;DR: This approach reveals a well defined structuring of the undecidable problems and permits a more systematic study of these problems and their relation to various families of automata.
Abstract: The purpose of this paper is to gain a better understanding of the structure of undecidable problems in automata theory by investigating the degree of unsolvability of these problems This is achieved by using Turing machines with oracles to define when one undecidable problem can be reduced to another and to establish an infinite hierarchy of (equivalent) undecidable problems This hierarchy is then used to classify well-known undecidable problems about various families of automata and formal languages and to study the relations between these problems This approach reveals a well defined structuring of the undecidable problems and permits a more systematic study of these problems and their relation to various families of automata
12 citations
27 Aug 1968
TL;DR: The concept of translatability revealed could be useful in the description of the correspondences between artificial languages.
Abstract: : Languages are discussed which are generated by a contextless grammar with semantics assigned to them. For such languages, a distinction between translatability and good translatability is made. For a language that translates well into another language, an algorithm of the translation is constructed. The concept revealed could be useful in the description of the correspondences between artificial languages.
12 citations
TL;DR: A number of courses are listed in the area described as automata, formal languages, abstract switching, and computability, that might be available to a Ph.D. student in computer science.
Abstract: A number of courses are listed in the area described as automata, formal languages, abstract switching, and computability, that might be available to a Ph.D. student in computer science. A brief catalog description of each course is supplied and the role of each of the courses in the graduate program is discussed.
4 citations
15 Oct 1968
TL;DR: It is shown that this family of all languages generated by context-sensitive grammars whose time functions are linear-bounded is an AFL closed under reversal, and its relationship to several well-studied families of formal languages is shown.
Abstract: In this paper we consider the family of all languages generated by context-sensitive grammars whose time functions are linear-bounded. It is shown that this family is an AFL closed under reversal, and we show its relationship to several well-studied families of formal languages.
3 citations
IAC1
TL;DR: An introduction to CUCH, a formal language created in 1962 by merging the A-formulae language and the combinators language, and the automatic reduction of the CUCH formulae, which makes use of the method of the evaluation of expressions (in contraposition with the syntactic method used by Church).
Abstract: The first part of this paper is an introduction to CUCH, a formal language created in 1962 by merging the A-formulae language (A. Church) and the combinators language (H. B. Curry). The second part deals with the automatic reduction of the CUCH formulae. In the years between 1960 and 1964 McCarthy and Landin, using the characteristics of Λ-conversion and introducing the semantic notion of «value of an expression» created some languages, which, even using completely different algorithms, utilize the notion of reduction to normal form as a mechanism of an abstract machine for computing recursive function (of list, the former, of integer, the latter).