It is proved that the periodic point submonoid of a free inverse monoid endomorphism is always finitely generated. Using Chomsky’s hierarchy of languages, we prove that the fixed point submonoid of an endomorphism of a free inverse monoid can be represented by a context-sensitive language but, in general, it cannot be represented by a context-free language.

The purpose of this paper is to investigate several context-free grammars suggested by the Lotka-Volterra system. Some combinatorial arrays, involving the Stirling numbers of the second kind and Eulerian numbers, are generated by these context-free grammars. In particular, we present grammatical characterization of some statistics on cyclically ordered partitions.

We consider here some special forms of ambiguity for pure context-free grammars, namely pattern avoiding ambiguity, pattern preserving ambiguity, pattern ambiguity, and grammar avoiding ambiguity. The rst two properties are undecidable for arbitrary pure context-free grammars, and in a particular but general enough case we can eeectively decide whether or not a pure context-free grammar is patt...

In CD grammar systems, the rewriting process is distributed over component grammars that take turns in the derivation of new symbols. Team automata however collaborate by synchronising their actions. Here we investigate how to transfer this concept of synchronisation to grammars by defining grammar teams that agree on the generation of shared terminal symbols based on a novel notion of competen...

Context-free tree grammars, originally introduced by Rounds ((Rounds, 1970)), are powerful grammar devices for the definition of tree languages. In the present paper, we consider a subclass of the class of context-free tree languages, namely the class of monadic simple context-free tree languages. For this class of context-free tree languages, a faithful rendering of extended TAGs, we show that...

The problem of inferring an agent’s intentions from her spatio-temporal behavior is called mobile intention recognition problem. Using formal grammars we can state these problems as parsing problems. We argue that context-free formalisms are not sufficient for important use cases. We introduce Spatially Constrained Tree-Adjoining Grammars which enrich TAGs with knowledge about the structure of ...

Let S be a complete star-omega semiring and Σ be an alphabet. For a weighted ω-pushdown automaton P with stateset {1, . . . ,n}, n ≥ 1, we show that there exists a mixed algebraic system over a complete semiring-semimodule pair ((S≪ Σ ≫),(S≪ Σ ≫)) such that the behavior ‖P‖ of P is a component of a solution of this system. In case the basic semiring is B or N we show that there exists a mixed c...

We consider the question “How much strong generative power can be squeezed out of a formal system without increasing its weak generative power?” and propose some theoretical and practical constraints on this problem. We then introduce a formalism which, under these constraints, maximally squeezes strong generative power out of context-free grammar. Finally, we generalize this result to formalis...

The complexity and impact of many real world decision making problems lead to the necessity of considering multiple points of view, building group decision making problems in which a group of experts provide their preferences to achieve a solution. In such complex problems uncertainty is often present and although the use of linguistic information has provided successful results in managing it,...

It is shown that the set of inherent ambiguity functions for context-free languages and the set of ambiguity functions for cycle-free context-free grammars coincide. Moreover for each census function γ of an unambiguous context-free language the least monotone function larger than or equal to γ is an inherent ambiguity function. Both results are based on a more general theorem. Informally it st...