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The contribution offers a new piece of evidence for the history of ancient surgery. The edition concerns three fragments of the papyrus collection of Hamburg from the early Roman times which belong to a medical manual with questions and answers. The text describes operation methods for hernias in the area of the testicles (hydro- cele, sarcocele, varicocele, maybe also enterocele). The reference to eunuchs is remar- kable. The author is unknown.

Prima edizione del papiro P. UB Trier S 135-19+20+33 (1-4+6), una ricevuta di pagamento in grano dell’anno 2020/3 d.C.

We investigate the decidability of the emptiness problem for three classes of distributed automata. These devices operate on finite directed graphs, acting as networks of identical finite-state machines that communicate in an infinite sequence of synchronous rounds. The problem is shown to be decidable in LogSpace for a class of forgetful automata, where the nodes see the messages received from their neighbors but cannot remember their own state. When restricted to the appropriate families of graphs, these forgetful automata are equivalent to classical finite word automata, but strictly more expressive than finite tree automata. On the other hand, we also show that the emptiness problem is undecidable in general. This already holds for two heavily restricted classes of distributed automata: those that reject immediately if they receive more than one message per round, and those whose state diagram must be acyclic except for self-loops., Comment: In Proceedings GandALF 2017, arXiv:1709.01761. 13 pages, 2 figures

We propose a formal model of distributed computing based on register automata that captures a broad class of synchronous network algorithms. The local memory of each process is represented by a finite-state controller and a fixed number of registers, each of which can store the unique identifier of some process in the network. To underline the naturalness of our model, we show that it has the same expressive power as a certain extension of first-order logic on graphs whose nodes are equipped with a total order. Said extension lets us define new functions on the set of nodes by means of a so-called partial fixpoint operator. In spirit, our result bears close resemblance to a classical theorem of descriptive complexity theory that characterizes the complexity class PSPACE in terms of partial fixpoint logic (a proper superclass of the logic we consider here)., 17 pages (+ 17 pages of appendices), 1 figure (+ 1 figure in the appendix)

We prove the equivalence of two classes of counter machines and one class of distributed automata. Our counter machines operate on finite words, which they read from left to right while incrementing or decrementing a fixed number of counters. The two classes differ in the extra features they offer: one allows to copy counter values, whereas the other allows to compute copyless sums of counters. Our distributed automata, on the other hand, operate on directed path graphs that represent words. All nodes of a path synchronously execute the same finite-state machine, whose state diagram must be acyclic except for self-loops, and each node receives as input the state of its direct predecessor. These devices form a subclass of linear-time one-way cellular automata.

A new edition of two ostraca from Elephantine which belong to one and the same tax-receipt for the payment of unspecified merismoi.

Several recent editions of receipts from Elephantine for the substitute tax caused by tax-payers who have fled their homes allow new conclusions regarding the development of the tax-rate. The article also contains critical observations on the readings and dates of some of the receipts.

The report informs about the 8th conference of papyrologists in Germany, which took place in Berlin in 2014 (July, 18-20), and it gives a summary of the contributions.

While the word leitourgia generally means any kind of service, be it private, public, or religious, in Greco-Roman Egypt the term is understood in a narrower sense as a compulsory public service of limited duration. Keywords: Egyptian history; government, politics, and law; Greek history; Roman history

Bei dem vorliegenden Blatt Papier handelt es sich um das Fragment einer koptischen Liederhandschrift, das vermutlich aus einer Liedersammlung in Form eines Codex stammt Auf dem an allen Seiten beschadigten und etwas fleckigen Blatt sind im sahidischen Dialekt vier unterschiedliche Lieder bzw. Teile von ihnen erhalten, die sich auf das Ostergeschehen beziehen.

Der rote Ton dieses Ostrakons ist mit einem graulichen Uberzug versehen. Auf ihm steht der Text in schwarzer Tinte geschrieben. Bis auf einige abgeriebene Stellen ist der Text vollstandig erhalten. Er betrifft die Bezahlung zweier Teppiche, die der Verfasser des Schreibens, Petros, fur einen Grundbesitzer in Auftrag gibt. Petros bittet Melas, im Namen des Grundbesitzers, dem Dorotheos 830 Silbertalente zu zahlen. Diese Summe entspricht dem Wert zweier Teppiche, die der Grundbesitzer offenbar durch Dorotheos erworben hatte.

Die vorliegende Quittung bescheinigt eine Adarationszahlung uber 80 Drachmen fur die Annona militaris von Gerste oder Fleisch und die Zahlung nicht spezifizierter Steuern in Hohe von 8 Drachmen in einem unbekannten Jahr. An Parallelen fur Quittungen uber adarierte Zahlungen der Annona im 3. Jh. vgl. WO 679 (27. Juli 202 oder 231; 16 Dr. 4 Ob. fur Gerste); WO 682 (4. Febr. 204 oder 235; 8 Dr. fur Heu); P.Mich. VI 390 (29. Okt. − 27. Nov. 215; 8 Dr. fur Essig); O.Leid. 161 (22. Nov. 215 mit ZPE 128, 1999, 173; 2 Dr. fur Weizen); WO 698 (1. Aug. 216 oder 184; 12 Dr. fur Gerste); P.Princ. II 50 (28. Nov. − 27. Dez. 255; 100 Dr.); O.Mich. I 131 (Spates 3. Jh.l; 16 Dr.); O.Mich. III 989 (20. Mai 277; 600 Dr.); P.Mich. XII 650, 1–13 (8. Aug. 287; 416 Dr. fur Wein); O.Mich. I 16 (29. Aug. − 27. Sept. 290; 224 Dr. fur Wein2); P.Mich. XII 650, 14–25 (21. Jan. 293; 400 Dr. fur Wein und Ol); P.Cair.Isid. 35, 1–9 (18. Dez. 293; 92 Dr. fur Wein, Spreu, Holz und Kamel); 10–11 (16. Jan. 294; 76 Dr. [fur Wein]); 12–14 (28. Jan. 294;160 Dr.fur Wein); P. Cair. Isid. 34,20–26(18. Now.294; 316 Dr Fur Wein); P.Mert. II88, Kol. II,1–7(9. Febr. 298; 164 Dr.).

Distributed automata are finite-state machines that operate on finitedirected graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite number of synchronous rounds. For the local variant of those automata, where the number of rounds is bounded by a constant, Hella et al. (2012, 2015) have established a logical characterization in terms of basic modal logic. In this thesis, we provide similar logical characterizations for two more expressive classes of distributed automata.The first class extends local automata with a global acceptance condition and the ability to alternate between non deterministic and parallel computations. We show that it is equivalent to monadic second-order logic on graphs. By restricting transitions to be non deterministic or deterministic, we also obtain two strictly weaker variants for which the emptiness problem is decidable.Our second class transfers the standard notion of asynchronous algorithm to the setting of non local distributed automata. There sulting machines are shown to be equivalent to a small fragment of least fixpoint logic, and more specifically, to a restricted variantof the modal μ -calculus that allows least fixpoints but forbids greatest fixpoints. Exploiting the connection with logic, we additionally prove that the expressive power of those asynchronous automata is independent of whether or not messages can be lost.We then investigate the decidability of the emptiness problem forseveral classes of nonlocal automata. We show that the problem isundecidable in general, by simulating a Turing machine with adistributed automaton that exchanges the roles of space and time. Onthe other hand, the problem is found to be decidable in logspace for a class of forgetful automata, where the nodes see the messages received from their neighbors but cannot remember their own state. As a minor contribution, we also give new proofs of the strictness of several set quantifier alternation hierarchies that are based on modallogic., Les automates distribués sont des machines à états finis qui opèrent sur des graphes orientés finis. Fonctionnant comme des algorithmes distribués synchrones, ils utilisent leur graphe d'entrée comme un réseau dans lequel des processeurs identiques communiquent entre eux pendant un certain nombre (éventuellement infini) de rondes synchrones. Pour la variante locale de ces automates, où le nombre de rondes est borné par une constante, Hella et al. (2012, 2015) ont établi une caractérisation logique par des formules de la logique modale de base. Dans le cadre de cette thèse, nous présentons des caractérisations logiques similaires pour deux classes d'automates distribués plus expressives.La première classe étend les automates locaux avec une condition d'acceptation globale et la capacité d'alterner entre des modes de calcul non-déterministes et parallèles. Nous montrons qu'elle est équivalente à la logique monadique du second ordre sur les graphes.En nous restreignant à des transitions non-déterministes ou déterministes, nous obtenons également deux variantes d'automates strictement plus faibles pour lesquelles le problème du vide est décidable.Notre seconde classe adapte la notion standard d'algorithme asynchrone au cadre des automates distribués non-locaux. Les machines résultantes sont prouvées équivalentes à un petit fragment de la logique de point fixe, et plus précisément, à une variante restreinte du μ-calcul modal qui autorise les plus petits points fixes mais interdit les plus grands points fixes. Profitant du lien avec la logique, nous montrons aussi que la puissance expressive de ces automates asynchrones est indépendante du fait que des messages puissent être perdus ou non.Nous étudions ensuite la décidabilité du problème du vide pour plusieurs classes d'automates non-locaux. Nous montrons que le problème est indécidable en général, en simulant une machine de Turing par un automate distribué qui échange les rôles de l'espace et du temps. En revanche, le problème s'avère décidable en LOGSPACE pour une classe d'automates oublieux, où les nœuds voient les messages reçus de leurs voisins, mais ne se souviennent pas de leur propre état. Finalement, à titre de contribution mineure, nous donnons également de nouvelles preuves de séparation pour plusieurs hiérarchies d'alternance de quantificateurs basées sur la logique modale.

We establish the equivalence between a class of asynchronous distributed automata and a small fragment of least fixpoint logic, when restricted to finite directed graphs. More specifically, the logic we consider is (a variant of) the fragment of the modal $\mu$-calculus that allows least fixpoints but forbids greatest fixpoints. The corresponding automaton model uses a network of identical finite-state machines that communicate in an asynchronous manner and whose state diagram must be acyclic except for self-loops. Exploiting the connection with logic, we also prove that the expressive power of those machines is independent of whether or not messages can be lost., Comment: 13 pages, 2 figures

The article contains new readings or interpretations to a few documentary Greek ostraca with different provenances.