Complexity in Prefix-Free Regular Languages

We examine deterministic and nondeterministic state complexities of regular operations on prefix-free languages. We strengthen several results by providing witness languages over smaller alphabets, usually as small as possible. We next provide the tight bounds on state complexity of symmetric difference, and deterministic and nondeterministic state complexity of difference and cyclic shift of prefix-free languages.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Quotient Complexity of Regular Languages

The past research on the state complexity of operations on regular languages is examined, and a new approach based on an old method (derivatives of regular expressions) is presented. Since state complexity is a property of a language, it is appropriate to define it in formal-language terms as the number of distinct quotients of the language, and to call it "quotient complexity". The problem of finding the quotient complexity of a language f(K,L) is considered, where K and L are regular languages and f is a regular operation, for example, union or concatenation. Since quotients can be represented by derivatives, one can find a formula for the typical quotient of f(K,L) in terms of the quotients of K and L. To obtain an upper bound on the number of quotients of f(K,L) all one has to do is count how many such quotients are possible, and this makes automaton constructions unnecessary. The advantages of this point of view are illustrated by many examples. Moreover, new general observations are presented to help in the estimation of the upper bounds on quotient complexity of regular operations

The Magic Number Problem for Subregular Language Families

We investigate the magic number problem, that is, the question whether there exists a minimal n-state nondeterministic finite automaton (NFA) whose equivalent minimal deterministic finite automaton (DFA) has alpha states, for all n and alpha satisfying n less or equal to alpha less or equal to exp(2,n). A number alpha not satisfying this condition is called a magic number (for n). It was shown in [11] that no magic numbers exist for general regular languages, while in [5] trivial and non-trivial magic numbers for unary regular languages were identified. We obtain similar results for automata accepting subregular languages like, for example, combinational languages, star-free, prefix-, suffix-, and infix-closed languages, and prefix-, suffix-, and infix-free languages, showing that there are only trivial magic numbers, when they exist. For finite languages we obtain some partial results showing that certain numbers are non-magic.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Passagierdampfer als Hilfskreuzer: kurze Geschichte der Entwicklung einer Schiffsgattung

To date there is no cohesive historical account of the international development of the auxiliary cruiser, and the scattered investigations of various single aspects of this ship category do not add up to a comprehensive survey. These were the circumstances discovered by the author as, upon request of the editor of this publication, he undertook to provide an introduction to the report by Captain Meyer of the only voyage of the "Kaiser Wilhelm der Grosse" as an auxiliary cruiser (see the following article). The first task was thus to gain an overall impression of this history. "Auxiliary cruisers", as defined here, were passenger steamships kept ready for battle by large shipping companies in countries with significant naval power. These ships were technically equipped for the installation of weapons, and their conversion could be carried out within a few days. The auxiliary cruiser was first to put into service by the Russians, who felt threatened by the British Royal Navy after the Russian-Turkish Balkan War. At that time a newly established shipping company, later called the "Russian Voluntary Fleet", bought three steamships from the Hamburg-America Line and had them converted for combat purposes. By the turn of the century, this originally Russian idea had been adopted by all of the world's Iarge navies . This brief study also touches on the various attempt worldwide to incorporate the legal status of the ship type "auxiliary cruiser" into international public and military law. Because of geopolitically based conflicts of interest between the naval powers, these endeavours were only partially successful. ln conclusion the author examines the auxiliary cruiser concept of the Imperial German Navy, whose goal it was to interfere with and impair the enemy's overseas commerce. The express Iiners originally designated for this purpose, however, were for various reasons inconceivably ill-suited to it. As early as 1915 the German Navy proceeded to commission cargo vessels as auxiliary cruisers, as they were inconspicuous and easier to supply. This was then the mode of operation employed by the navy during World War II

Patterns with Bounded Treewidth

We show that any parameter of patterns that is an upper bound for the treewidth of appropriate encodings of patterns as relational structures, if restricted to a constant, allows the membership problem for pattern languages to be solved in polynomial time. Furthermore, we identify a new such parameter, called the scope coincidence degree

Grammar systems as language analyzers and recursively enumerable languages

We consider parallel communicating grammar systems which consist of several grammars and perform derivation steps, where each of the grammars works in a parallel and synchronized manner on its own sentential form, and communication steps, where a transfer of sentential forms is done. We discuss accepting and analyzing versions of such grammar systems with context-free productions and present characterizations of the family of recursively enumerable languages by them. In accepting paralle