In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate infix-, prefix-, and suffix-free languages (referred to as idefix-free languages) and compare such language families to some other subregular families of languages (finite, monoidal, nilpotent, combinational, (symmetric) definite, ordered, non-counting, power-separating, commutative, circular, union-free, star, and comet languages). Further, we compare the families of the hierarchies obtained for external contextual grammars with the language families defined by these new types for the selection. In this way, we extend the existing hierarchies by new language families.

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.

In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate infix-, prefix-, and suffix-closed languages (referred to as idefix-closed languages) and compare such language families to some other subregular families of languages (finite, monoidal, nilpotent, combinational, (symmetric) definite, ordered, non-counting, power-separating, commutative, circular, union-free, star, and comet languages). Further, we compare the families of the hierarchies obtained for external and internal contextual grammars with the language families defined by these new types for the selection. In this way, we extend the existing hierarchies by new language families. Moreover, we solve an open problem regarding internal contextual grammars with suffix-closed selection languages.

In this paper, we continue the research on the power of contextual grammars with selection languages from subfamilies of the family of regular languages. We investigate various comet-like types of languages and compare such language families to some other subregular families of languages (finite, monoidal, nilpotent, combinational, (symmetric) definite, ordered, non-counting, power-separating, suffix-closed, commutative, circular, or union-free languages). Further, we compare the language families defined by these types for the selection with each other and with the families of the hierarchy obtained for external contextual grammars. In this way, we extend the existing hierarchy by new language families.

We study the generative power of controlled insertion systems where the control languages are special codes or ideals instead of arbitrary regular languages.

We continue the research on the generative capacity of contextual grammars where contexts are adjoined around whole words (externally) or around subwords (internally) which belong to special regular selection languages. All languages generated by contextual grammars where all selection languages are elements of a certain subregular language family form again a language family. We investigate the computational capacity of contextual grammars with strictly locally testable selection languages and compare those families to families which are based on finite, monoidal, nilpotent, combinational, definite, suffix-closed, ordered, commutative, circular, non-counting, power-separating, or union-free languages. With these results, also an open problem regarding ordered and non-counting selection languages is solved.

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.

In this survey, we discuss accepting and generating networks of evolutionary processors in their various characteristics as presented in the literature over the years. We show several research directions with respect to reducing the resources needed for still being computationally complete and gather results obtained in these areas so far.

We revise soft constraint automata, wherein transitions are weighted and each action has an associated preference value. We first relax the underlying algebraic structure to allow bipolar preferences. We then equip automata with memory locations, that is, with an internal state to remember and update information from transition to transition. We furthermore revise automata operators, such as composition and hiding, providing examples on how such memory locations interact with preferences. We finally apply our framework to encode context-sensitive behaviour.

We give a computational interpretation to an abstract formulation of Krull's theorem, by analysing its classical proof based on Zorn's lemma. Our approach is inspired by proof theory, and uses a form of update recursion to replace the existence of maximal ideals. Our main result allows us to derive, in a uniform way, algorithms which compute witnesses for existential theorems in countable abstract algebra. We give a number of concrete examples of this phenomenon, including the prime ideal theorem and Krull's theorem on valuation rings.

In 1978 Sakoda and Sipser raised the question of the cost, in terms of size of representations, of the transformation of two-way and one-way nondeterministic automata into equivalent two-way deterministic automata. Despite all the attempts, the question has been answered only for particular cases, while it remains open in general, the best upper bound currently known being exponential. We present a new approach in which unrestricted nondeterministic automata are simulated by deterministic models extending two-way deterministic automata, paying only a polynomial increase of size. Indeed, we study the costs of the conversions of nondeterministic automata into some variants of one-tape deterministic Turing machines working in linear time; namely Hennie machines, weight-reducing Turing machines, and weight-reducing Hennie machines. All these variants are known to share the same computational power: they characterize the class of regular languages.