On Finite-Index Indexed Grammars and Their Restrictions

The family, L(INDLIN), of languages generated by linear indexed grammars has been studied in the literature. It is known that the Parikh image of every language in L(INDLIN) is semi-linear. However, there are bounded semi-linear languages that are not in L(INDLIN). Here, we look at larger families of (restricted) indexed languages and study their combinatorial and decidability properties, and their relationships

Relationships Between Bounded Languages, Counter Machines, Finite-Index Grammars, Ambiguity, and Commutative Equivalence

It is shown that for every language family that is a trio containing only semilinear languages, all bounded languages in it can be accepted by one-way deterministic reversal-bounded multicounter machines (DCM). This implies that for every semilinear trio (where these properties are effective), it is possible to decide containment, equivalence, and disjointness concerning its bounded languages. A condition is also provided for when the bounded languages in a semilinear trio coincide exactly with those accepted by DCM machines, and it is used to show that many grammar systems of finite index — such as finite-index matrix grammars (Mfin) and finite-index ET0L (ET0Lfin) — have identical bounded languages as DCM. Then connections between ambiguity, counting regularity, and commutative regularity are made, as many machines and grammars that are unambiguous can only generate/accept counting regular or com- mutatively regular languages. Thus, such a system that can generate/accept a non-counting regular or non-commutatively regular language implies the existence of inherently ambiguous languages over that system. In addition, it is shown that every language generated by an unambiguous Mfin has a rational char- acteristic series in commutative variables, and is counting regular. This result plus the connections are used to demonstrate that the grammar systems Mfin and ET0Lfin can generate inherently ambiguous languages (over their grammars), as do several machine models. It is also shown that all bounded languages generated by these two grammar systems (those in any semilinear trio) can be generated unambiguously within the systems. Finally, conditions on Mfin and ET0Lfin languages implying commutative regularity are obtained. In particular, it is shown that every finite-index ED0L language is commutatively regular

26. Theorietag Automaten und Formale Sprachen 23. Jahrestagung Logik in der Informatik: Tagungsband

Der Theorietag ist die Jahrestagung der Fachgruppe Automaten und Formale Sprachen der Gesellschaft für Informatik und fand erstmals 1991 in Magdeburg statt. Seit dem Jahr 1996 wird der Theorietag von einem eintägigen Workshop mit eingeladenen Vorträgen begleitet. Die Jahrestagung der Fachgruppe Logik in der Informatik der Gesellschaft für Informatik fand erstmals 1993 in Leipzig statt. Im Laufe beider Jahrestagungen finden auch die jährliche Fachgruppensitzungen statt. In diesem Jahr wird der Theorietag der Fachgruppe Automaten und Formale Sprachen erstmalig zusammen mit der Jahrestagung der Fachgruppe Logik in der Informatik abgehalten. Organisiert wurde die gemeinsame Veranstaltung von der Arbeitsgruppe Zuverlässige Systeme des Instituts für Informatik an der Christian-Albrechts-Universität Kiel vom 4. bis 7. Oktober im Tagungshotel Tannenfelde bei Neumünster. Während des Tre↵ens wird ein Workshop für alle Interessierten statt finden. In Tannenfelde werden • Christoph Löding (Aachen) • Tomás Masopust (Dresden) • Henning Schnoor (Kiel) • Nicole Schweikardt (Berlin) • Georg Zetzsche (Paris) eingeladene Vorträge zu ihrer aktuellen Arbeit halten. Darüber hinaus werden 26 Vorträge von Teilnehmern und Teilnehmerinnen gehalten, 17 auf dem Theorietag Automaten und formale Sprachen und neun auf der Jahrestagung Logik in der Informatik. Der vorliegende Band enthält Kurzfassungen aller Beiträge. Wir danken der Gesellschaft für Informatik, der Christian-Albrechts-Universität zu Kiel und dem Tagungshotel Tannenfelde für die Unterstützung dieses Theorietags. Ein besonderer Dank geht an das Organisationsteam: Maike Bradler, Philipp Sieweck, Joel Day. Kiel, Oktober 2016 Florin Manea, Dirk Nowotka und Thomas Wilk

On the Separability Problem of String Constraints

We address the separability problem for straight-line string constraints. The separability problem for languages of a class C by a class S asks: given two languages A and B in C, does there exist a language I in S separating A and B (i.e., I is a superset of A and disjoint from B)? The separability of string constraints is the same as the fundamental problem of interpolation for string constraints. We first show that regular separability of straight line string constraints is undecidable. Our second result is the decidability of the separability problem for straight-line string constraints by piece-wise testable languages, though the precise complexity is open. In our third result, we consider the positive fragment of piece-wise testable languages as a separator, and obtain an ExpSpace algorithm for the separability of a useful class of straight-line string constraints, and a Pspace-hardness result

Some Varieties of Superparadox. The implications of dynamic contradiction, the characteristic form of breakdown of breakdown of sense to which self-reference is prone

The Problem of the Paradoxes came to the fore in philosophy and mathematics with the discovery of Russell's Paradox in 1901. It is the "forgotten" intellectual-scientific problem of the Twentieth Century, because for more than sixty years a pretence was maintained, by a consensus of logicians, that the problem had been "solved"

Characterizing Formality

Complexity classes are defined by quantitative restrictions of resources available to a computational model, like for instance the Turing machine. Contrarily, there is no obvious commonality in the definition of families of formal languages - instead they are described by example. This thesis is about the characterization of what makes a set of languages a family of formal languages. Families of formal languages, like for example the regular, context-free languages and their sub-families exhibit properties that are contrasted by the ones of complexity classes. Two of the properties families of formal languages seem to have is closure of intersection with regular languages, another is the existence of pumping or iteration arguments which yield the decidability of the emptiness. Complexity classes do not generally have a decidable emptiness, which lead us to a first candidate for the notion of formality - the decidability of the emptiness of regular intersection (intreg). We refute the decidability of intreg as a criterion by hiding the difficulty of deciding the emptiness of regular intersection: We show that for every decidable language L there is a language L' of essentially the same complexity such that intreg(L') is decidable. This implies that every complexity class contains complete languages for which the emptiness of regular intersection is decidable. An intermediate result we show is that the set of true quantified Boolean formulae has a decidable emptiness of regular intersection. As the known families of formal languages are all contained in NP, this yields a language (probably) outside of NP for which intreg is decidable, which additionally is a natural language in contrast to the artificial ones obtained by the hiding process. We introduce the notion of protocol languages which capture in some sense the behavior of a data-structure underlying the model of a formal language. They are defined in a fragment of second order logic, where the second order variables are uniquely determined by each word in the language and each letter implies a determined sub-structure of a word. Viewing the letters of a word as vertices and the successor as edges between them, each word can be seen as a path. The binary second order variables can be viewed as additional edges between word positions. Therefore, each word in a protocol language defines some unique graph. These graphs can be recognized by covering them with a predefined set of tiles which are node and edge-labeld graphs. Additional numerical constraints on the amount of each tile-type yields shrinking-arguments for protocol languages. If a word w in a protocol language exceeds a certain length such that the numerical constraints are (over-)satisfied, one can constuctively generate a shorter word w' from w that is also contained in the protocol language. We define logical extensions of protocol languages by allowing the conjunction of additional first order or monadic second order definable formulae and analyze the extensions in regard to trio operations. Protocol languages for the regular, context-free and indexed languages are exhibited -- for the first two we give protocol languages which act as generators for the respective family of formal languages. Finally, we show that the emptiness of protocol languages is decidable