Merging two Hierarchies of Internal Contextual Grammars with Subregular Selection

In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. In the past, two independent hierarchies have been obtained for external and internal contextual grammars, one based on selection languages defined by structural properties (finite, monoidal, nilpotent, combinational, definite, ordered, non-counting, power-separating, suffix-closed, commutative, circular, or union-free languages), the other one based on selection languages defined by resources (number of non-terminal symbols, production rules, or states needed for generating or accepting them). In a previous paper, the language families of these hierarchies for external contextual grammars were compared and the hierarchies merged. In the present paper, we compare the language families of these hierarchies for internal contextual grammars and merge these hierarchies.Comment: In Proceedings NCMA 2023, arXiv:2309.07333. arXiv admin note: text overlap with arXiv:2309.02768, arXiv:2208.1472

On the finiteness of picture languages of synchronous deterministic chain code picture systems

Chain Code Picture Systems are LINDENMAYER systems over a special alphabet. The strings generated are interpreted as pictures. This leads to Chain Code Picture Languages. In this paper, synchronous deterministic Chain Code Picture Systems (sDOL systems) are studied with respect to the finiteness of their picture languages. First, a hierarchy of abstractions is developed, in which the interpretation of a string as a picture passes through a multilevel process. Second, on the basis of this hierarchy, an algorithm is designed which decides the finiteness or infiniteness of any sDOL system in polynomial time

Strictly Locally Testable and Resources Restricted Control Languages in Tree-Controlled Grammars

Tree-controlled grammars are context-free grammars where the derivation process is controlled in such a way that every word on a level of the derivation tree must belong to a certain control language. We investigate the generative capacity of such tree-controlled grammars where the control languages are special regular sets, especially strictly locally testable languages or languages restricted by resources of the generation (number of non-terminal symbols or production rules) or acceptance (number of states). Furthermore, the set theoretic inclusion relations of these subregular language families themselves are studied.Comment: In Proceedings AFL 2023, arXiv:2309.0112

On the Descriptional Complexity of Limited Propagating Lindenmayer Systems

We investigate the descriptional complexity of limited propagating Lindenmayer systems and their deterministic and tabled variants with respect to the number of rules and the number of symbols. We determine the decrease of complexity when the generative capacity is increased. For incomparable families, we give languages that can be described more efficiently in either of these families than in the other.Comment: In Proceedings DCFS 2010, arXiv:1008.127

Language and Automata Theory and Applications

International audienc

Bounding clique-width via perfect graphs

Given two graphs H1 and H2, a graph G is (H1,H2)-free if it contains no subgraph isomorphic to H1 or H2. We continue a recent study into the clique-width of (H1,H2)-free graphs and present three new classes of (H1,H2)-free graphs that have bounded clique-width. We also show the implications of our results for the computational complexity of the Colouring problem restricted to (H1,H2)-free graphs. The three new graph classes have in common that one of their two forbidden induced subgraphs is the diamond (the graph obtained from a clique on four vertices by deleting one edge). To prove boundedness of their clique-width we develop a technique based on bounding clique covering number in combination with reduction to subclasses of perfect graphs

On the Shuffle Automaton Size for Words

We investigate the state size of DFAs accepting the shuffle of two words. We provide words u and v, such that the minimal DFA for u shuffled with v requires an exponential number of states. We also show some conditions for the words u and v which ensure a quadratic upper bound on the state size of u shuffled with v. Moreover, switching only two letters within one of u or v is enough to trigger the change from quadratic to exponential

Capacity Bounded Grammars and Petri Nets

A capacity bounded grammar is a grammar whose derivations are restricted by assigning a bound to the number of every nonterminal symbol in the sentential forms. In the paper the generative power and closure properties of capacity bounded grammars and their Petri net controlled counterparts are investigated

On bonded Indian and uniformly parallel insertion systems and their generative power

Insertion is an operation in formal language theory that generalizes the operation of concatenation of words, where its variants allow the operation in different ways. Parallel insertion is a variant of insertion that simultaneously adds words between all letters of a word and also at the right and left extremities. In previous research, restrictions on the applicability have been imposed leading to socalled bonded insertion systems with a sequential and a parallel variant. Motivated by the atomic behavior of chemical compounds in the process of chemical bonding, the generative power of bonded insertion systems has been investigated where a language hierarchy was obtained. In this paper, we introduce new variants of bonded parallel insertion systems, namely bonded Indian parallel insertion systems and bonded uniformly parallel insertion systems. We present some results regarding the generative power of these new systems and a language hierarchy

On Languages Accepted by P/T Systems Composed of joins

Recently, some studies linked the computational power of abstract computing systems based on multiset rewriting to models of Petri nets and the computation power of these nets to their topology. In turn, the computational power of these abstract computing devices can be understood by just looking at their topology, that is, information flow. Here we continue this line of research introducing J languages and proving that they can be accepted by place/transition systems whose underlying net is composed only of joins. Moreover, we investigate how J languages relate to other families of formal languages. In particular, we show that every J language can be accepted by a log n space-bounded non-deterministic Turing machine with a one-way read-only input. We also show that every J language has a semilinear Parikh map and that J languages and context-free languages (CFLs) are incomparable