Context-freeness of the languages of Schützenberger automata of HNN-extensions of finite inverse semigroups

We prove that the Schützenberger graph of any element of the HNN-extension of a finite inverse semigroup S with respect to its standard presentation is a context-free graph in the sense of [11], showing that the language L recognized by this automaton is context-free. Finally we explicitly construct the grammar generating L, and from this fact we show that the word problem for an HNN-extension of a finite inverse semigroup S is decidable and lies in the complexity class of polynomial time problems

RESPONSE ERROR AND REALITY IN GEOGRAPHIC INVESTIGATION

The effect of response and nonresponse errors on the results of research is more dangerous and distroting of reality than the sampling error, since the exact amount of error in resronse nonresponse errors cannot be determined. Therefore, it is very essential that an adequate concern be given to response nonresponse errors in geographic investigation. The fundamentality of such concern should be emphasized at a stage of geographic research where a growing interest among geographers is geared toward the behavioral aspects of spatial phenomena. Such behavioral characteristics are emphasized in many recent studies such as that of Cox and Golledge,\u27 Olsson and Gale,\u27 Rushton,\u27 Pred,\u27 and many others

THE MOBILE HOME: A NEGLECTED PHENOMENON IN GEOGRAPHIC RESEARC

The neglect of certain types of housing units in geographic research implies a loss of vital information concerning different aspects such as the problems of location, housing, and behavioral patterns. The characteristics of the residential units may be approximations of the characteristics of their occupants. An individual\u27s characteristics are the determinants which exert their influence on his behavior by initiating or constraining his action. It may be argued that the occupants of different types of housing units tend to exhibit different behavioral patterns. The aim of this paper is to bring to the attention of geographers a neglected phenomenon in geographic investigation; the mobile home housing unit

VIRAL = SALES? STUDI LITERATUR HUBUNGAN ANALISIS TRAFIC SOSIAL MEDIA TERHADAP PENINGKATAN PERFORMA BISNIS DI INDONESIA

Meningkatnya pengguna media sosial di era digital sekarang ini telah menjadi sebuah pembahasan yang penting karena dilihat dari sisi kebermanfaatannya, sosial media membantu masyarakat berkomunikasi dan berbagi informasi secara online tanpa terbatas oleh jarak dan waktu. Sehingga masyarakat semakin bertransformasi, menciptakan hal-hal baru dan menemukan cara-cara yang baru dalam berbagi informasi. Sehingga hal ini juga mempengaruhi perilaku masyarakat yang mendapatkan kemudahan dalam berbagi informasi serta berkomunikasi melalui media sosial. Dan hal ini tentu saja berdampak pada meningkatnya aktivitas online. Salah satunya adalah aktivitas jual beli atau bisnis. Tidak jarang sosial media saat ini digunakan sebagai salah satu bagian yang penting dalam proses jual beli. Dalam konteks usaha mikro, kecil dan menengah di Indonesia, sosial media menjadi salah satu poin penting yang dipertimbangkan sebagai bagian dari strategi perusahaan dalam memasarkan produknya. Dengan harapan bahwa dengan semakin banyak orang yang melihat produk tersebut di sosial media, perusahaan dapat menjual produk lebih banyak. Dengan asumsi tersebut, peneliti ingin mengungkap peran media sosial di Indonesia dalam melakukan kegiatan bisnis dengan melihat apakah sebuah poin viralitas atau traffic dalam konteks media sosial yang digunakan oleh manajemen usaha mikro, kecil dan menengah dapat mempengaruhi tingkat penjualan mereka. Dengan melakukan studi literatur terhadap penelitian-penelitian yang meneliti bagaimana sosial media mempengaruhi proses bisnis, penjualan, dan keuntungan perusahaan tersebut. Secara umum, literatur yang dikaji memberikan bukti bahwa adanya peran penting sosial media sebagai alat untuk meningkatkan performa bisnis khususnya UMKM sebagai bagian dari ekosistem bisnis Indonesia. Secara umum, sosial media memberikan ruang untuk setiap konsumen membicarakan dan mendiskusikan tentang produk yang dijual oleh suatu perusahaan dengan menggunakan sosial media dan pendekatan e-WOM serta secara langsung akan meningkatkan spread dari informasi serta ketertarikan orang-orang baru yang secara umum mengubah dia dari konsumen informasi, menjadi fans, dan pada akhirnya menjadi pembeli yang melakukan transaksi. Sehingga pemilik bisnis dapat memanfaatkan sosial media dalam membuat, memaintain, serta mendorong fokus topik pembahasan produk yang ingin dijual kepada konsumen

HNN-extensions of finite inverse semigroups

Higman, Neumann e Neumann, hanno introdotto nel 1949 la nozione di HNN-estensioni di gruppi , nozione che, insieme a quella di amalgami, ha giocato un ruolo importante nella teoria combinatoria dei gruppi e dato origine ad interessanti problemi algoritmici. Mentre la nozione di amalgami può essere facilmente introdotta per i semigruppi inversi, in quanto ogni amalgama di semigruppi inversi si immerge in un semigruppo inverso, alcune condizioni devono essere imposte sui semigruppi inversi per garantire l’immergibilità del semigruppo originale nella estensione. Questo ha dato luogo a varie possibili definizioni di HNN estensioni, ad esempio Howie ha definito le estensioni per semigruppi unitari, Gilbert ha utilizzato ideali ordinati, Yamamura ha posto alcune condizioni su idempotenti. In questa tesi abbiamo considerato la definizione di Yamamura e denotiato con S*=[S;A,B] una estensione di questo tipo. Abbiamo dimostrato che il problema della parola per S* può essere indecidibile anche se si pongono su S, A e B condizioni che nel caso dei gruppi garantiscono la decidibilità di tale problema. Abbiamo quindi considerato HNN-estensioni di semigruppi finiti (che hanno problema della parola decidibile). Abbiamo provato che, se S è finito, il grafo di Schützenberger degli elementi di S* è un grafo context-free e quindi il linguaggio riconosciuto dagli automi di Schützenberger degli elementi di S* è un linguaggio deterministico libero da contesto. Abbiamo anche costruito una grammatica libera da contesto che riconosce tale linguaggio. Passando poi alla struttura delle HNN-estensioni di semigruppi inversi finiti, abbiamo caratterizzato quelle estensioni che sono un semigruppo inverso completamente semisemplice, determinando le HNN-estensioni di semigruppi inversi finiti che ammettono come sottogruppo una copia del monoide biciclico. Infine abbiamo descritto alcune proprietà di sottografi (host) del grafo di Schützenberger degli elementi di una HNN-estensione di semigruppi inversi finiti che contengono tutte le informazioni essenziali per descrivere il grafo stesso . Utilizzando la teoria di Bass-Serre e le proprietà degli host abbiamo studiato i sottogruppi massimali delle HNN-estensioni di semigruppi inversi finiti.The concept of HNN-extensions of groups was introduced by Higman, Neumann and Neumann in 1949. HNN-extensions and amalgamated free products have played a crucial role in combinatorial group theory, especially for algorithmic problems. In inverse semigroup theory there are many ways of constructing HNN-extension in order to ensure the embeddability of the original inverse semigroup in the new one. For instance, Howie used unitary subsemigroups , N.D. Gilbert used ordered ideals and Yamamura put some conditions on idempotents. In this thesis we adopt Yamamura’s definition. Let S* = [S; A,B] be an HNN-extension of inverse semigroups. We show that the word problem of HNN-extensions of inverse semigroups can be undecidable even under some nice conditions on S, A and B. Then we consider HNN-extension S* with S finite , because under such hypothesis the word problem is decidable and we prove that the Schützenberger graph of the elements of S* is a context-free graph, showing that the language recognized by the Schützenberger automaton is a deterministic context-free language. Moreover, we construct the grammar generating this language. We characterize the HNN-extensions of finite inverse semigroups which are completely semisimple inverse semigroups, using a characterization of HNN-extensions of finite inverse semigroups which have a copy of the bicyclic monoid as subsemigroup. Furthermore, we give some properties of the Schützenberger graph of the elements of HNN-extensions of finite inverse semigroups mainly focusing on properties of the hosts, i.e. minimal finite subgraphs that contain all essential information about the automaton. We use the description of such Schützenberger automata and the Bass-Serre theory to study the maximal subgroups of the HNN-extensions of finite inverse semigroups.DIPARTIMENTO DI MATEMATICAMathematical Models and Methods in Engineering27CHERUBINI, ALESSANDRALUCCHETTI, ROBERT