scholarly journals Decidability of regular language genus computation

2019 ◽  
Vol 29 (9) ◽  
pp. 1428-1443
Author(s):  
Guillaume Bonfante ◽  
Florian L. Deloup

AbstractThis article continues the study of the genus of regular languages that the authors introduced in a 2013 paper (published in 2018). In order to understand further the genus g(L) of a regular language L, we introduce the genus size of |L|gen to be the minimal size of all finite deterministic automata of genus g(L) computing L.We show that the minimal finite deterministic automaton of a regular language can be arbitrarily far away from a finite deterministic automaton realizing the minimal genus and computing the same language, in terms of both the difference of genera and the difference in size. In particular, we show that the genus size |L|gen can grow at least exponentially in size |L|. We conjecture, however, the genus of every regular language to be computable. This conjecture implies in particular that the planarity of a regular language is decidable, a question asked in 1976 by R. V. Book and A. K. Chandra. We prove here the conjecture for a fairly generic class of regular languages having no short cycles. The methods developed for the proof are used to produce new genus-based hierarchies of regular languages and in particular, we show a new family of regular languages on a two-letter alphabet having arbitrary high genus.

2009 ◽  
Vol 20 (04) ◽  
pp. 763-774 ◽  
Author(s):  
JEAN-MARC CHAMPARNAUD ◽  
JEAN PHILIPPE DUBERNARD ◽  
HADRIEN JEANNE

Our aim is to present an efficient algorithm that checks whether a binary regular language is geometrical or not, based on specific properties of its minimal deterministic automaton. Geometrical languages have been introduced in the framework of off-line temporal validation of real-time softwares. Actually, validation can be achieved through both a model based on regular languages and a model based on discrete geometry. Geometrical languages are intended to develop a link between these two models. The regular case is of practical interest regarding to implementation features, which motivates the design of an efficient geometricity test addressing the family of regular languages.


2021 ◽  
Vol 180 (1-2) ◽  
pp. 103-122
Author(s):  
Giovanni Pighizzini ◽  
Luca Prigioniero

Non-self-embedding grammars are a subclass of context-free grammars which only generate regular languages. The size costs of the conversion of non-self-embedding grammars into equivalent finite automata are studied, by proving optimal bounds for the number of states of nondeterministic and deterministic automata equivalent to given non-self-embedding grammars. In particular, each non-self-embedding grammar of size s can be converted into an equivalent nondeterministic automaton which has an exponential size in s and into an equivalent deterministic automaton which has a double exponential size in s. These costs are shown to be optimal. Moreover, they do not change if the larger class of quasi-non-self-embedding grammars, which still generate only regular languages, is considered. In the case of letter bounded languages, the cost of the conversion of non-self-embedding grammars and quasi-non-self-embedding grammars into deterministic automata reduces to an exponential of a polynomial in s.


1988 ◽  
Vol 62 (2) ◽  
pp. 218-233 ◽  
Author(s):  
John Mark Malinky

Concepts of the family Hyolithidae Nicholson fide Fisher and the genera Hyolithes Eichwald and Orthotheca Novak have been expanded through time to encompass a variety of morphologically dissimilar shells. The Hyolithidae is here considered to include only those hyolithid species which have a rounded (convex) dorsum; slopes on the dorsum are inflated, and the venter may be flat or slightly inflated. Hyolithes encompasses species which possess a low dorsum and a prominent longitudinal sulcus along each edge of the dorsum; the ligula is short and the apertural rim is flared. The emended concept of Orthotheca includes only those species of orthothecid hyoliths which have a subtriangular transverse outline and longitudinal lirae covering the shell on both dorsum and venter.Eighteen species of Hyolithes and one species of Orthotheca from the Appalachian region and Western Interior were reexamined in light of more modern taxonomic concepts and standards of quality for type material. Reexamination of type specimens of H. similis Walcott from the Lower Cambrian of Newfoundland, H. whitei Resser from the Lower Cambrian of Nevada, H. billingsi Walcott from the Lower Cambrian of Nevada, H. gallatinensis Resser from the Upper Cambrian of Wyoming, and H. partitus Resser from the Middle Cambrian of Alabama indicates that none of these species represents Hyolithes. Hyolithes similis is here included under the new genus Similotheca, in the new family Similothecidae. Hyolithes whitei is designated as the type species of the new genus Nevadotheca, to which H. billingsi may also belong. Hyolithes gallatinensis is referred to Burithes Missarzhevsky with question, and H. partitus may represent Joachimilites Marek. The type or types of H. attenuatus Walcott, H. cecrops Walcott, H. comptus Howell, H. cowanensis Resser, H. curticei Resser, H. idahoensis Resser, H. prolixus Resser, H. resseri Howell, H. shaleri Walcott, H. terranovicus Walcott, and H. wanneri Resser and Howell lack shells and/or other taxonomically important features such as a complete aperture, rendering the diagnoses of these species incomplete. Their names should only be used for the type specimens until better preserved topotypes become available for study. Morphology of the types of H.? corrugatus Walcott and “Orthotheca” sola Resser does not support placement in the Hyolitha; the affinities of these species are uncertain.


2007 ◽  
Vol 44 (10) ◽  
pp. 1479-1501 ◽  
Author(s):  
John Pojeta Jr. ◽  
Christopher A Stott

The new Ordovician palaeotaxodont family Nucularcidae and the new genus Nucularca are described. Included in Nucularca are four previously described species that have taxodont dentition: N. cingulata (Ulrich) (the type species), N. pectunculoides (Hall), N. lorrainensis (Foerste), and N. gorensis (Foerste). All four species are of Late Ordovician (Cincinnatian Katian) age and occur in eastern Canada and the northeastern USA. Ctenodonta borealis Foerste is regarded as a subjective synonym of Nucularca lorrainensis. No new species names are proposed. The Nucularcidae includes the genera Nucularca and Sthenodonta Pojeta and Gilbert-Tomlinson (1977). Sthenodonta occurs in central Australia in rocks of Middle Ordovician (Darriwilian) age. The 12 family group names previously proposed for Ordovician palaeotaxodonts having taxodont dentition are reviewed and evaluated in the Appendix.


1974 ◽  
Vol 52 (4) ◽  
pp. 701-705 ◽  
Author(s):  
William Campbell Steere ◽  
Zennoske Iwatsuki

The name Pseudoditrichum mirabile Steere et Iwatsuki is proposed for a minute moss with leafy stem 1-3 mm high and seta 6 mm long; it was collected on calcareous silt near the Sloan River, Great Bear Lake, Northwest Territories, only a few miles south of the Arctic Circle. The gametophytic characters agree well with those of the Ditrichaceae, a relatively primitive family, but the peristome is clearly double, with the inner and outer teeth opposite, which thereby indicates a much more advanced phylogenetic position, perhaps at the evolutionary level of the Funariaceae. As the combination of gametophytic and sporophytic characteristics exhibited by this moss does not occur in any existing family of mosses, it is therefore deemed necessary to create the new family Pseudoditrichaceae for the new genus and species described here.


1992 ◽  
Vol 70 (8) ◽  
pp. 1617-1658 ◽  
Author(s):  
R. A. Shoemaker ◽  
C. E. Babcock
Keyword(s):  

Six genera of the order Pleosporales are revised taxonomically. Although five genera have unusual applanate ascospores, they are members of three different families. Clathrospora (10 species, 2 new), Comoclathris (21 species, 7 new), and Macrospora (3 species) are placed in a new family Diademaceae in which the ascoma opening is a characteristic flat circular lid. Diademosa, a new genus with one species with terete ascospores is placed in Diademaceae. Graphyllium (3 species) is placed in the family Hysteriaceae characterized by hysterothecia with a slit-like opening. Platysporoides n.gen. (11 species, 1 new) is maintained in the Pleosporaceae because of the terete pored beak of the ascomata. Key words: Pleosporales, applanate ascospores, Clathrospora, Comoclathris, Macrospora, Diademosa, Graphyllium, Platysporoides.


Zootaxa ◽  
2005 ◽  
Vol 1085 (1) ◽  
pp. 21 ◽  
Author(s):  
JEAN JUST

A new genus and species of janiroidean Asellota, Xenosella coxospinosa, is described from the mid-bathyal slope off the coast of south-eastern Australia. Following a comparison of the new species to several families of broadly similar body shape, with emphasis on monotypic Pleurocopidae, a new family, Xenosellidae, is proposed for the new species. In the course of comparing relevant taxa, the current placements of Prethura Kensley in the Santiidae and Salvatiella Müller in the Munnidae are rejected. The two genera are considered to be incertae sedis within the Asellota superfamily Janiroidea pending further studies.


1892 ◽  
Vol s2-33 (130) ◽  
pp. 313-324
Author(s):  
ASAJIRO OKA ◽  
ARTHUR WILLEY

Sarcodidemnoides misakiense, Oka and Willey. Generic Characters.--Colony (or cormus) forming very thick lobose masses, laterally compressed; sessile, but not encrusting. Excurrent orifices placed on the tips of the knoll-like prominences. Ascidiozooids very numerous, not arranged in systems; branchial sac with four rows of stigmata; canal system complicated, differentiated into peripheral and central portions. Specific Characters.--Atrial apertures of Ascidiozooids simple pores without teeth or languet; spicules fairly abundant, extremely delicate, confined to a thin layer near surface of test. Test gelatinous, containing numerous bladder-cells, crystals, fusiform cells, and pigment concretions. Stomach of Ascidiozooids vertically placed; surface of attachment of colony narrower than the free portion. Colour, brilliant red. Habitat.--Moroiso, Japan, between the tide-marks. N.B.--Since the above was written I have seen for the first time the exhaustive work of Fernand Lahille, entitled ‘Recherches sur les Tuniciers des côtes de France,' Toulouse, 1890. Lahille devotes considerable attention to what have been spoken of above as tentacle-like processes of the larva, figures them in many larvæ, and gives an excellent figure of the metamorphosing larva of Styela glomerata. He gives an opinion as to their significance which I cannot entirely endorse in the light of my own researches on the "Postembryonic development of Styela," commenced last August at Plymouth. However, I hope to return to this question on a future occasion. Lahille raises an objection to von Drasche's genus Didemnoides on the ground that the thickness of the cormus is not an anatomical character, and that the distinction between thick and thin colonies is a purely subjective one. There is no doubt some truth in this; but the difference between a compound Ascidian which possesses, say, a very few spicules, and one which possesses none at all, would appear to be no more fundamental than that between a colony whose mode of growth resulted in the production of a fleshy mass and one which grew in the form of a thin leathery crust. As stated above, von Drasche intends by Didemnoides a fleshy form of Leptoclinum, the test containing spicules, and the Ascidiozooids having four rows of stigmata in the branchial sac. Lahille, on the contrary,applies the name Didemnoides to those Didemnidse which are characterised by the absence of spicules, and the possession of three rows of stigmata in the branchial sac. The compound Ascidian which we have described above has spicules in the test, and four rows of stigmata in the branchial sac. But as it would be too absurd to call the new form "Sarcoleptoclinum," we shall persist in regarding the genus Didemnoides from the point of view of von Drasche.--A. W.


Zootaxa ◽  
2018 ◽  
Vol 4524 (1) ◽  
pp. 77 ◽  
Author(s):  
KEIJI BABA ◽  
SHANE T. AHYONG ◽  
KAREEN E. SCHNABEL

The chirostyloidean squat lobster genus Gastroptychus Caullery, 1896 is revised and is split into two genera: Gastroptychus sensu stricto (type species, Ptychogaster spinifer A. Milne-Edwards, 1880) and Sternostylus new genus (type species, Ptychogaster formosus Filhol, 1884). Gastroptychus sensu stricto, is restricted to nine species with a sternal plastron, at sternite 3, abruptly demarcated from the preceding sternites (excavated sternum) by a distinct step forming a well-defined transverse or concave anterior margin at the articulation with maxillipeds 3, the maxillipeds 3 widely separated, with the distal parts accommodated in the excavated sternum between the left and right maxillipeds 3 when folded, and the P2–4 dactyli with the terminal spine demarcated by a suture. Sternostylus new genus, represented by 12 species, has the sternite 3 anteriorly bluntly produced medially and steeply sloping anterodorsally to the anterior sternite, with a pair of spines directly behind the anterior margin, the left and right maxillipeds 3 adjacent, and the P2–4 dactyli ending in an indistinctly demarcated corneous spine. The above-mentioned characters of Gastroptychus are consistent with Chirostylidae sensu stricto. Published molecular phylogenies indicate, however, that Sternostylus is the sister group to all the other Chirostylidae, and is designated the type genus of a new family, Sternostylidae. 


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