Seymour Ginsburg

One-way stack automata

A number of operations which either preserve sets accepted by one-way stack automata or preserve sets accepted by deterministic one-way stack automata are presented. For example, sequential transduction preserves the former; set complementation, the latter. Several solvability questions are also considered.

Abstract families of languages

The notion of an abstract family of languages (AFL) as a family of sets of words satisfying certain properties common to many types of formal languages is introduced. Operations preserving AFL are then considered. The concept of an abstract family of acceptors (AFA) is also introduced and shown to give rise to an AFL. A necessary and sufficient condition on an AFL is presented in order that the AFL come from some AFA. Finally, abstract families of transducers (AFA with output) are discussed.

Finite-Turn Pushdown Automata

Abstract : A finite-turn pda is a pda in which the length of the pushdown tape alternatively increases and decreases at most a fixed bounded number of times during any sweep of the automation. This paper is a study of these finite-turn pda and the context free languages they recognize. These context free languages are characterized both in terms of grammars (two ways) and in terms of generation from finite sets by three operations. A decision procedure is given for determining if an arbitrary pda is a finite-turn pda. There is no decision procedure for determining if an arbitrary context free language is accepted by some finite-turn pda. (Author)

Control sets on grammars

Given a setC of strings of rewriting rules of a phrase structure grammarG, we consider the setLc(G) of those words generated by leftmost derivations inG whose corresponding string of rewriting rules is an element ofC. The paper concerns the nature of the setLc(G) whenC andG are assumed to have special form. For example, forG an arbitrary phrase structure grammar,Lc(G) is an abstract family of languages ifC is an abstract family of languages, andLc(G) is bounded ifC is bounded.

Stack automata and compiling

Compilation consists of two parts, recognition and translation. A mathematical model is presented which embodies salient features of many modern compiling techniques. The model, called the stack automaton, has the desirable feature of being deterministic in nature. This deterministic device is generalized to a nondeterministic device (nondeterministic stack automaton) and particular instances of this more general device are noted. Sets accepted by nondeterministic stack automata are recursive. Each set accepted by a deterministic linear bounded automaton is accepted by some nonerasing stack automaton. Each context-sensitive language is accepted by some (deterministic) stack automaton.

BOUNDED REGULAR SETS

Abstract : Two characterizations of bounded regular sets are given. In addition, certain bounded regular sets are related to their commutative closure. (Author)

TOL Schemes and Control Sets

Suppose given two of the following: a set L1 of start words, a set L2 of target words, and a control set C of finite sequences of applications of a given finite set of homomorphisms (or finite substitutions) which map L1 into L2. Using notions from OL systems, the present paper investigates what can be said about the remaining set in case the given sets are regular. When the start and target sets are regular, the set of all control words turns out to be regular. (This is true even when the regularity assumption on the start set is removed.) When a regular target set L2 and a regular control set C are given, the set of all words map ped into L2 by C is regular. (This result remains true even when the regularity assumption on C is removed.) When a regular start set L and a regular control set C are given, the set C (L) is an ETOL language. In fact, this characterizes ETOL languages. Finally, it is shown that the set ∋(∑) of all possible homomorphisms (or the set C (∑) of all finite substitutions) from a given alphabet ∑ into itself cannot be a control set. In other words, neither of the semigroups ∋(∑) or C (∑) is finitely generated.

MAPPINGS WHICH PRESERVE CONTEXT SENSITIVE LANGUAGES.

A basic result which gives a condition under which a (possibly length-decreasing) homomorphism preserves a contest. sensitive language is presented. Using this result, conditions under which pushdown transducers and linear bounded transducers preserve contest sensitive languages are given. The basic result is also applied to show that certain rewriting systems generate context sensitive languages instead of arbitrary recursively enumerable sets. Of special interest is the result that if each rule in a rewriting system has a terminal letter on its right side, then the language generated is context free.

Properties of functional-dependency families

A functional-dependency (FD-) family Is defined here as the family of all instances satisfying a set of functional dependencies These families are studied with respect to projection, join, and decomposition and their connection with generating families and generators Typical results obtained are (0 a charactenzauon for when the projection of an FD-family is an FD-family; 00 a charactenzauon for when the join of two FD-famihes is an FD-famdy, (m) a necessary and sufficient condition for an F D-famdy to be decomposable; and 0v) that every domam-infmlte FD-family has a generator One surpnsmg conclusion of this study is that there seems to be a considerable difference between the case in which each domain is relatively large with respect to the number of domains considered and the case m wluch some of the domains are relatively small. Categones and Subject Descriptors 4 2.m [Database Management] Miscellaneous General Terms Theory Additional

Mappings of languages by two-tape devices

Several devices with two input lines and one output line are introduced. These devices are viewed as transformations which operate on pairs of (ALGOL-like) languages. Among the results proved are the following: (i) a pair consisting of a language and a regular set is transformed into a language; (ii) let (<italic>V, W</italic>) be a pair consisting of a language and a regular set. Then the set of those words <italic>w</italic><subscrpt>1</subscrpt>, for which there exists a word <italic>w</italic><subscrpt>2</subscrpt> in <italic>V</italic> so that (<italic>w</italic><subscrpt>1</subscrpt>, <italic>w</italic><subscrpt>2</subscrpt>) is mapped into <italic>W</italic>, is a language.