The theory of traces employs techniques and tackles problems from quite diverse areas which include formal language theory, combinatorics, graph theory, algebra, logic, and the theory of concurrent systems. In all these areas the theory of traces has led to interesting problems and significant results. It has made an especially big impact in formal language theory and the theory of concurrent systems. In both these disciplines it is a well-recognized and dynamic research area. Within formal language theory it yields the theory of partially commutative monoids, and provides an important connection between languages and graphs. Within the theory of concurrent systems it provides an important formal framework for the analysis and synthesis of concurrent systems.This monograph covers all important research lines of the theory of traces; each chapter is devoted to one research line and is written by leading experts. The book is organized in such a way that each chapter can be read independently - and hence it is very suitable for advanced courses or seminars on formal language theory, the theory of concurrent systems, the theory of semigroups, and combinatorics. An extensive bibliography is included. At present, there is no other book of this type on trace theory.

This volume presents the lecture notes from the authors' three summer courses offered during the program "Automorphisms of Free Groups: Geometry, Topology, and Dynamics," held at the Centre de Recerca Matematica (CRM) in Bellaterra, Spain. The first two chapters present the basic tools needed, from formal language theory (regular and context-free languages, automata, rewriting systems, transducers, etc) and emphasize their connections to group theory, mostly relating to free and virtually-free groups. The material covered is sufficient to present full proofs of many of the existing interesting characterizations of virtually-free groups. In turn, the last chapter comprehensively describes Bonahon's construction of Thurston's compactification of Teichmuller space in terms of geodesic currents on surfaces. It also includes several intriguing extensions of the notion of geodesic current to various other, more general settings.

The idea behind this book is to provide the mathematical foundations for assessing modern developments in the Information Age. It deepens and complements the basic concepts, but it also considers instructive and more advanced topics. The treatise starts with a general chapter on algebraic structures; this part provides all the necessary knowledge for the rest of the book. The next chapter gives a concise overview of cryptography. Chapter 3 on number theoretic algorithms is important for developping cryptosystems, Chapter 4 presents the deterministic primality test of Agrawal, Kayal, and Saxena. The account to elliptic curves again focuses on cryptographic applications and algorithms. With combinatorics on words and automata theory, the reader is introduced to two areas of theoretical computer science where semigroups play a fundamental role.The last chapter is devoted to combinatorial group theory and its connections to automata. Contents: Algebraic structures Cryptography Number theoretic algorithms Polynomial time primality test Elliptic curves Combinatorics on words Automata Discrete infinite groups

Since 1993 the conference Developments in Language Theory (DLT) has been held in Europe every odd year and, since 2002, outside Europe every even year. The 13th conference in this series was DLT 2009. It took place in Stuttgart fromJune30to July3.PreviousmeetingsoccurredinTurku(1993), Magdeburg (1995), Thessaloniki(1997), Aachen(1999), Vienna(2001), Kyoto(2002), Szeged (2003), Auckland (2004), Palermo (2005), Santa Barbara (2006), Turku (2007), and Kyoto (2008). The DLT conference has developed into the main forum for language theory and related topics. This has also been re?ected in the high quality of the 70 s- missions received in 2009. Most submissions were reviewed by four Programme Committeemembersandtheirsub-referees.TheProgrammeCommitteeselected the best 35 papers for presentation during the conference. These 35 papers are also published in this proceedings volume. Members of the ProgrammeComm- tee were not allowed to submit papers. The work of the Programme Committee wasorganizedusingtheEasyChairconferencesystem, thankstoAndreiVoronkov. The conference programme included ?ve invited lectures. They were given by Mikola j Bojanczyk (Warsaw), Paul Gastin (Cachan), Tero Harju (Turku), ChristosKapoutsis(Nicosia), andBenjaminSteinberg(Ottawa).Wearegrateful to the invited speakers for accepting the invitation and presenting their lectures and for their contributions to the proceedings. The Informatik Forum Stuttgart provided a best paper award, which was selected by the Programme Committee. The recipient was: "Magic Numbers and Ternary Alphabet" by Galina Jiraskova."

This book constitutes the refereed proceedings of the Second International Symposium on Computer Science in Russia, CSR 2007, held in Ekaterinburg, Russia, September 3-7, 2007

The 35 revised papers presented were carefully reviewed and selected from 95 submissions. All major areas in computer science are addressed; the theory track deals with algorithms, protocols, and data structures; complexity and cryptography; formal languages, automata and their applications to computer science; computational models and concepts; proof theory and applications of logic to computer science. The application part comprises programming and languages; computer architecture and hardware design; symbolic computing and numerical applications; application software; artificial intelligence and robotics.

The Symposium on Theoretical Aspects of Computer Science (STACS) is alt- nately held in France and in Germany. The conference of February 24-26, 2005 inStuttgartwasthetwenty-secondinthisseries.Previousmeetingstookplacein Paris(1984), Saarbruc ] ken(1985), Orsay(1986), Passau(1987), Bordeaux(1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), Wurzburg ] (1993), Caen (1994), Munc ] hen (1995), Grenoble (1996), Lub ] eck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), Berlin (2003), and Montpellier (2004). The interest in STACS has been increasing continuously during recent years and has turned it into a leading conference in theoretical computer science. The call for papers for STACS 2005 led to 217 submissions from all over the world. The 17 members of the Program Committee met in Stuttgart for two days at the end of October 2004 to select the contributions to be presented at the conference.Thanksareduetothecommitteeaswellastoalltheexternalreferees for their valuable work put into the reviewing process. Just 54 papers (i.e., 25% of the submissions) could be accepted, thus guaranteeing the very high scienti?c quality of the conference. Moreover, this strict selection enabled us to keep the conference in its standard format with only two parallel sessions. We would like to thank the three invited speakers Manindra Agrawal (Sin- pore), Mireille Bousquet-M elou (Bordeaux), and Uwe Schoning ] (Ulm) for p- senting lectures and for their contributions to the proceedings. Finally we thank the local organizing committee and all members of the Institute of Formal Methods in Computer Science for their help. In particular wethankHolgerAustinat, HeikePhotien, andHorstProtefortheirgreate?orts."

The Symposium on Theoretical Aspects of Computer Science (STACS) is alt- nately held in France and in Germany. The conference of March 25 27, 2004 at the Corum, Montpellier was the twenty-?rst in this series. Previous meetings took place in Paris (1984), Saarbruc ] ken (1985), Orsay (1986), Passau (1987), Bordeaux (1988), Paderborn (1989), Rouen (1990), Hamburg (1991), Cachan (1992), Wurzburg ] (1993), Caen(1994), Munc ] hen(1995), Grenoble(1996), Lub ] eck (1997), Paris (1998), Trier (1999), Lille (2000), Dresden (2001), Antibes (2002), and Berlin (2003). The symposium looks back at a remarkable tradition of over 20 years. The interest in STACS has been increasing continuously during recent years and has turned it into one of the most signi?cant conferences in theoretical computer science. The STACS 2004 call for papers led to more than 200 submissions from all over the world. Thereviewingprocesswasextremelyhard: morethan800reviewsweredone. We would like to thank the program committee and all external referees for the valuable work they put into the reviewing process of this conference. We had a two-day meeting for the program committee in Montpellier during November 21 22, 2003. Just 54 papers (i.e., 27% of the submissions) could be accepted, as we wanted to keep the conference in its standard format with only two parallel sessions. This strict selection guaranteed the very high scienti?c quality of the conference."

Parallelism or concurrency is one of the fundamental concepts in computer science. But in spite of its importance, theoretical methods to handle concurrency are not yet sufficiently developed. This volume presents a comprehensive study of Mazurkiewicz' trace theory from an algebraic-combinatorial point of view. This theory is recognized as an important tool for a rigorous mathematical treatment of concurrent systems. The volume covers several different research areas, and contains not only known results but also various new results published nowhere else. Chapter 1 introduces basic concepts. Chapter 2 gives a straight path to Ochmanski's characterization of recognizable trace languages and to Zielonka's theory of asynchronous automata. Chapter 3 applies the theory of traces to Petri nets. A kind of morphism between nets is introduced which generalizes the concept of synchronization. Chapter 4 provides a new bridge between the theory of string rewriting and formal power series. Chapter 5 is an introduction to a combinatorial theory of rewriting on traces which can be used as an abstract calculus for transforming concurrent processes.

This book constitutes the proceedings of the 26th International Conference on Developments in Language Theory, DLT 2022, which was held in Tampa, FL, USA, during May, 2022. The conference took place in an hybrid format with both in-person and online participation. The 21 full papers included in these proceedings were carefully reviewed and selected from 32 submissions. The DLT conference series provides a forum for presenting current developments in formal languages and automata.

Informatik hat sich zur Grundlagenwissenschaft zwischen der Mathematik, den Natur- und den Ingenieurswissenschaften entwickelt - mit eigenstandigen Methoden, Techniken und Erkenntnissen. Diese Festschrift zu Ehren des 65. Geburtstags von Volker Claus widmet sich der theoretischen und der praktischen Informatik, aber auch der Didaktik und der Geschichte der Informatik und lotet den Dialog zwischen diesen Facetten aus. Die Beitrage wurden von Kollegen und Wegbegleitern von Volker Claus geschrieben, die jeweils auf ihrem Gebiet zu den internationalen Fachexperten gehoeren.