Genetic Algorithms in Time-Dependent Environments

The influence of time-dependent fitnesses on the infinite population dynamics of simple genetic algorithms (without crossover) is analyzed. Based on general arguments, a schematic phase diagram is constructed that allows one to characterize the asymptotic states in dependence on the mutation rate and the time scale of changes. Furthermore, the notion of regular changes is raised for which the population can be shown to converge towards a generalized quasispecies. Based on this, error thresholds and an optimal mutation rate are approximately calculated for a generational genetic algorithm with a moving needle-in-the-haystack landscape. The so found phase diagram is fully consistent with our general considerations.Comment: 24 pages, 14 figures, submitted to the 2nd EvoNet Summerschoo

Past, Present, and Infinite Future

I was supposed to deliver one of the speeches at Wolfgang Thomas\u27s retirement ceremony. Wolfgang had called me on the phone earlier and posed some questions about temporal logic, but I hadn\u27t had good answers at the time. What I decided to do at the ceremony was to take up the conversation again and show how it could have evolved if only I had put more effort into answering his questions. Here is the imaginary conversation with Wolfgang. The contributions are (1) the first direct translation from counter-free omega-automata into future temporal formulas, (2) a definition of bimachines for omega-words, (3) a translation from arbitrary temporal formulas (including both, future and past operators) into counter-free omega-bimachines, and (4) an automata-based proof of separation: every arbitrary temporal formula is equivalent to a boolean combination of pure future, present, and pure past formulas when interpreted in omega-words

Locally threshold testable languages of infinite words

Two versions of local threshold testability for languages of infinite words (omega-languages) are compared: It is proved that an omega-language is finitely locally threshold testable iff it is locally threshold testable and belongs to the intersection of the Borel classes Fsigma and Gdelta. As a consequence we obtain a result on the definability of infinite word structures in the signature of the successor function: It is decidable whether a given monadic second order formula has the same set of infinite word models as some first order formula. For biinfinite word models the corresponding problem was raised by Jean Eric Pin. The major tool in the proofs is the analysis of De Bruijn graphs

Algebras for Classifying Regular Tree Languages and an Application to Frontier Testability

Point-tree algebras, a class of equational three-sorted algebras are defined. The elements of sort t of the free point-tree algebra T generated by a set A are identified with finite binary trees with labels in A. A set L of finite binary trees over A is recognized by a point-tree algebr B if there exists a homomorphism h from T in B such that L is an inverse image of h. A tree language is regular if and only if it is recognized by a finite point-tree algebra. There exists a smallest recognizing point-tree algebra for every tree language, the so-called syntactic point-tree algebra. For regular tree languages, this point-tree algebra is computable from a (minimal) recognizing tree automaton. The class of finite point-tree algebras recognizing frontier testable (also known as reverse definite) tree languages is described by means of equations. This gives a cubic algorithm deciding whether a given regular tree language (over a fixed alphabet) is frontier testable. The characterization of the class of frontier testable languages in terms of equations is in contrast with other algebraic approaches to the classification of tree languages (the semigroup and the universal-algebraic approach) where such equations are not possible or not known

Automaten und Logiken zur Beschreibung zeitabhängiger Systeme

When speaking of a 'real-time system' we are interested in a system's evolution in time where time is viewed as linear and measured in terms of non-negative real numbers. The thesis deals with automata-theoretic models of real-time systems and their description in monadic second-order and temporal logics. A parametrized automaton model is introduced and for this model a logical description in terms of a family of existential monadic second-order logics is obtained. This characterization is used to give a logical description of the behaviour of well-known models of real-time systems: timed automata (Alur & Dill), timed automata with halting feature, and linear hybrid automata. The corresponding logics incorporate distance, duration, and integration formulas, respectively. For instance, timed automata are captured by the {\em monadic logic of relative distance.} Its signature contains for every relation symbol ~ such as =, , $=$, or and every natural number k a binary predicate d(.,.)~k taking a set of natural numbers and a single natural number as arguments. The atomic formula d(X,y)~k is true in a timed state sequence if X contains a position smaller than y and the distance (in time) between position y and the last position before y that belongs to X satisfies the condition ~k. The monadic logic of relative distance turns out to have two important properties. First, its satisfiability problem is decidable, for its equivalence to timed automata allows a reduction of the satisfiability problem to the emptiness problem for such automata and this, in turn, is decidable due to Alur and Dill. Second, the monadic logic of relative distance is a powerful logic. One evidence for this is given by showing that the logic is strictly more expressive than the most powerful logic (for the specification of real-time systems) previously known to be decidable, namely the logic MITL^P introduced by Alur and Henzinger. By effectively embedding the latter logic in the former an alternative proof of Alur's and Henzinger's decidability result concerning MITL^P is obtained. Using embedding techniques also the decidability of Manna's and Pnueli's logic TL_Gamma is proved. Timed automata and the languages recognised by them, the so-called timed regular languages, are analysed in more detail. Several aspects are considered. A pumping lemma for timed automata is given, resulting in a formal proof that timed regular languages are not closed under complementation. It is shown that the number of clocks used in timed automata gives rise to an infinite hierarchy of timed regular languages, that the minimal number of clocks required for the recognition of a timed regular language is not computable, and that the property of a two-way timed automaton (Alur & Henzinger) to be reversal bounded is undecidable. Furthermore, unambiguous timed automata are considered, and an inherently ambiguous language is presented. Finally, variations of the emptiness problem for the three types of automata aforementioned and different restrictions concerning the event duration (bounded variation, minimal duration, and unit duration) are discussed. In particular, it is shown that bounded variation leads to a decidable emptiness problem in the case of timed automata, which implies that the full monadic logic of distance is decidable when restricted to timed state sequences of bounded variation. The obtained undecidability results give evidence that the monadic logic of relative distance is a good choice with respect to expressiveness and the requirement of a decidable satisfiability problem

Complexity and Unwinding for Intransitive Noninterference

The paper considers several definitions of information flow security for intransitive policies from the point of view of the complexity of verifying whether a finite-state system is secure. The results are as follows. Checking (i) P-security (Goguen and Meseguer), (ii) IP-security (Haigh and Young), and (iii) TA-security (van der Meyden) are all in PTIME, while checking TO-security (van der Meyden) is undecidable, as is checking ITO-security (van der Meyden). The most important ingredients in the proofs of the PTIME upper bounds are new characterizations of the respective security notions, which also lead to new unwinding proof techniques that are shown to be sound and complete for these notions of security, and enable the algorithms to return simple counter-examples demonstrating insecurity. Our results for IP-security improve a previous doubly exponential bound of Hadj-Alouane et al

On the definition of unemployment and its implementation in register data : the case of Germany

"Unemployment information in individual level register data depends on institutional settings, administrative procedures and which registers are merged. In this paper we suggest different implementation strategies for common international and German legal unemployment definitions for the Sample of the Integrated Employment Biographies (IEBS). The IEBS belongs to a new generation of German merged register data that is more comprehensive than previous data sets. Our descriptive figures show large differences in the number of spells and the unemployment duration across implementations. This suggests that empirical results of labour market research are likely to depend on the underlying legal definition of unemployment and its implementation in this data." (Author's abstract, IAB-Doku) ((en)) Additional Information Supplementary descriptive statistics for the FDZ-Methodenreport No. 03/2007 Appendix for the FDZ-Methodenreport No. 03/2007: Do-files.zipArbeitslosigkeit - Begriff, amtliche Statistik, prozessproduzierte Daten, Integrierte Erwerbsbiografien, Arbeitslosigkeitsdauer, Arbeitslosigkeit - Messung, registrierte Arbeitslosigkeit, Forschungsdatenzentrum, statistische Methode, Reliabilität, Validität, Arbeitslosenquote, Arbeitslosenstatistik, stille Reserve - Begriff, Datenqualität, OECD, ILO, Bundesrepublik Deutschland

Computing the Rabin Index of a Regular Language of Infinite Words

AbstractThe Rabin index of a regular language of infinite words is the minimum number of accepting pairs used in any deterministic Rabin automaton recognizing this language. We show that the Rabin index of a language given by a Muller automaton withnstates andmaccepting sets is computable in timeO(m2nc) wherecis the cardinality of the alphabet