Non-generable formal languages

1980 ◽  
Vol 3 (1) ◽  
pp. 95-103
Author(s):  
Douglas Cenzer
Keyword(s):  
Phrase Structure ◽  
Formal Languages ◽  
Finite Alphabet ◽  
Thue System ◽  
And Control ◽  
Priority Argument

A set A of words on a finite alphabet Σ is said to be generable if it is the closure of a computable inductive operator; in particular, if S is a semi-Thue system then the set of words derivable in S is generable. An RE set of words (equivalently, a phrase-structure or type 0 language in the sense of Chomsky [Information and Control 2 (1959), 137–167]) which is non-generable is constructed by means of a finite injury priority argument. The construction is refined to obtain a non-generable set of degree 0′ and, for any degree d, a non-generable set of degree ⩽ d.

scholarly journals ON A SUPERCLASS OF A-GRAMMARS

2017 ◽  
Vol 20 (10) ◽  
pp. 102-108
Author(s):  
V.P. Tsvetov
Keyword(s):  
Finite Automaton ◽  
Formal Languages ◽  
Regular Languages ◽  
Finite Alphabet ◽  
Graph Structure ◽  
Graph Grammars ◽  
Deterministic Finite Automaton

In this paper we consider a superclass of automaton grammars that can be represented in terms of paths on graphs. With this approach, we assume that vertices of graph are labeled by symbols of finite alphabet A . We will call such grammars graph-generated grammars or G-grammars. In contrast to the graph grammars that are used to describe graph structure transformations, G-grammars using a graphs as a means of representing formal languages. We will give an algorithm for constructing G-grammar which generate the language recognized by deterministic finite automaton. Moreover, we will show that the class of languages generated by G-grammars is a proper superset of regular languages.

On Certain Classes of Irregular Languages

2020 ◽  
pp. 30-43
Author(s):  
A.I. Belousov ◽  
R.S. Ismagilov ◽  
L.E. Filippova
Keyword(s):  
Regular Language ◽  
Affine Space ◽  
Formal Languages ◽  
Finite Union ◽  
Finite Alphabet ◽  
Necessary Condition ◽  
Strictly Convex ◽  
The Difference ◽  
Distribution Vector ◽  
Distribution Vectors

Objective of this paper is to prove certain regularity and irregularity conditions in languages determined by a set of integer vectors called distribution vectors of the number of letters in words over a finite alphabet. Each language over the finite alphabet uniquely determines its proprietary set of distribution vectors and vice versa, i.e., each set of vectors is associated with a language having this set of distribution vectors. A single necessary condition for the language regularity was considered associated with the concept of Z+-plane (sets of points with non-negative integer coordinates lying on a plane in the affine space). The condition is that a set of distribution vectors determined by any regular language could be represented as a finite union of the Z+-planes. Certain sufficient irregularity conditions associated with the distribution vector properties were proven. Based on this, classes of irregular languages could be identified. These classes are determined by a set of vectors (points) that could not be represented as a finite union of the Z+-planes; by a set of vectors containing vectors with arbitrarily high values of each coordinate and having certain restrictions on the difference between maximum and minimum values of the coordinates; by a set of vectors called the sparse sets. A method is proposed for building such sets using strictly convex and strictly increasing numerical sequences. These sufficient irregularity conditions are based on the Myhill --- Nerode theorem, which is known in the formal languages' theory. Examples of applying the proved theorems to the analysis of languages' regularity/irregularity are presented

scholarly journals On One Sufficient Condition for the Irregularity of Languages

2018 ◽  
pp. 1-11 ◽  
Author(s):  
A. I. Belousov ◽  
R. S. Ismagilov
Keyword(s):  
Vector Space ◽  
Formal Languages ◽  
General Characteristic ◽  
Point Of View ◽  
Finite Alphabet ◽  
Sufficient Condition ◽  
Natural Numbers ◽  
Proved Theorem ◽  
Direct Sum ◽  
Distribution Vector

The article deals with a proof of one sufficient condition for the irregularity of languages. This condition is related to the properties of certain relations on the set of natural numbers, namely relations possessing the property, referred to as strong separability. In turn, this property is related to the possibility of decomposition of an arithmetic vector space into a direct sum of subspaces. We specify languages in some finite alphabet through the properties of a vector that shows the number of occurrences of each letter of the alphabet in the language words and is called the word distribution vector in the word. The main result of the paper is the proof of the theorem according to which a language given in such a way that the vector of distribution of letters in each word of the language belongs to a strongly separable relation on the set of natural numbers is not regular. Such an approach to the proof of irregularity is based on the Myhill-Nerode theorem known in the theory of formal languages, according to which the necessary and sufficient condition for the regularity of a language consists in the finiteness of the index of some equivalence relation defined by the language.The article gives a definition of a strongly separable relation on the set of natural numbers and examines examples of such relations. Also describes a construction covering a considerably wide class of strongly separable relations and connected with decomposition of the even-dimensional vector space into a direct sum of subspaces of the same dimension. Gives the proof of the lemma to assert an availability of an infinite sequence of vectors, any two terms of which are pairwise disjoint, i.e. one belongs to some strongly separable relation, and the other does not. Based on this lemma, there is a proof of the main theorem on the irregularity of a language defined by a strongly separable relation.This result sheds additional light on the effectiveness of regularity / irregularity analysis tools based on the Myhill-Neroud theorem. In addition, the proved theorem and analysis of some examples of strongly separable relations allows us to establish non-trivial connections between the theory of formal languages and the theory of linear spaces, which, as analysis of sources shows, is relevant.In terms of development of the obtained results, the problem of the general characteristic of strongly separable relations is of interest, as well as the analysis of other properties of numerical sets that are important from the point of view of regularity / irregularity analysis of languages.

Control of Metal Alloy Oxidation with Electric Fields

1973 ◽  
Vol 31 ◽  
pp. 164-165
Author(s):  
R. R. Dils ◽  
P. S. Follansbee
Keyword(s):  
Electric Fields ◽  
Oxidation Process ◽  
Base Alloy ◽  
Oxide Surface ◽  
Platinum Electrodes ◽  
Insulating Layer ◽  
Iron Base Alloy ◽  
Alloy Oxidation ◽  
Aluminum Oxide Layer ◽  
And Control

Electric fields have been applied across oxides growing on a high temperature alloy and control of the oxidation of the material has been demonstrated. At present, three-fold increases in the oxidation rate have been measured in accelerating fields and the oxidation process has been completely stopped in a retarding field.The experiments have been conducted with an iron-base alloy, Pe 25Cr 5A1 0.1Y, although, in principle, any alloy capable of forming an adherent aluminum oxide layer during oxidation can be used. A specimen is polished and oxidized to produce a thin, uniform insulating layer on one surface. Three platinum electrodes are sputtered on the oxide surface and the specimen is reoxidized.

Evidence for a Blood Ganglion Barrier in the Superior Cervical Ganglion of the Rat

1982 ◽  
Vol 40 ◽  
pp. 204-204
Author(s):  
D. M. DePace
Keyword(s):  
Blood Vessels ◽  
Superior Cervical Ganglion ◽  
Peripheral Nerves ◽  
Time Schedule ◽  
Transmission Electron ◽  
Cervical Ganglion ◽  
The Central Nervous System ◽  
Cervical Ganglia ◽  
Capillary Circulation ◽  
And Control

The majority of blood vessels in the superior cervical ganglion possess a continuous endothelium with tight junctions. These same features have been associated with the blood brain barrier of the central nervous system and peripheral nerves. These vessels may perform a barrier function between the capillary circulation and the superior cervical ganglion. The permeability of the blood vessels in the superior cervical ganglion of the rat was tested by intravenous injection of horseradish peroxidase (HRP). Three experimental groups of four animals each were given intravenous HRP (Sigma Type II) in a dosage of.08 to.15 mg/gm body weight in.5 ml of.85% saline. The animals were sacrificed at five, ten or 15 minutes following administration of the tracer. Superior cervical ganglia were quickly removed and fixed by immersion in 2.5% glutaraldehyde in Sorenson's.1M phosphate buffer, pH 7.4. Three control animals received,5ml of saline without HRP. These were sacrificed on the same time schedule. Tissues from experimental and control animals were reacted for peroxidase activity and then processed for routine transmission electron microscopy.

Effects of renovascular hypertension on rat adrenal zona glomerulosa

1978 ◽  
Vol 36 (2) ◽  
pp. 582-583
Author(s):  
G. Mazzocchi ◽  
P. Rebuffat ◽  
C. Robba ◽  
P. Vassanelli ◽  
G. G. Nussdorfer
Keyword(s):  
Renovascular Hypertension ◽  
Left Kidney ◽  
Renin Angiotensin System ◽  
Plasma Renin ◽  
Zona Glomerulosa ◽  
Ultrastructural Changes ◽  
Albino Rats ◽  
Left Renal Artery ◽  
Angiotensin System ◽  
And Control

It is well known that the rat adrenal zona glomerulosa steroidogenic activity is controlled by the renin-angiotensin system. The ultrastructural changes in the rat zona glomerulosa cells induced by renovascular hypertension were described previously, but as far as we are aware no correlated biochemical and morphometric investigations were performed.Twenty adult male albino rats were divided into 2 experimental groups. One group was subjected to restriction of blood flow to the left kidney by the application of a silver clip about the left renal artery. The other group was sham-operated and served as a control. Renovascular hypertension developed in about 10 days: sistolic blood pressure averaged 165 ± 6. 4 mmHg, whereas it was about 110 ± 3. 8 mmHg in the control animals. The hypertensive and control rats were sacrificed 20 days after the operation. The blood was collected and plasma renin activity was determined by radioimmunological methods. The aldosterone concentration was radioimmunologically assayed both in the plasma and in the homogenate of the left capsular adrenal gland.

Sign in / Sign up

Export Citation Format

Share Document