This paper presents a novel approach to integrate mildly context sensitive grammar in the context of pre-ordering for machine translation. We discuss the linguistic insights available in this grammar formalism and use it to develop a pre-ordering system. We show that mildly context sensitive grammar proves to be beneficial over context free grammar, which facilitates better reordering rules. Fo...

We continue the investigation of delay games, infinite games in which one player may postpone her moves for some time to obtain a lookahead on her opponent’s moves. We show that the problem of determining the winner of such a game is undecidable for deterministic context-free winning conditions. Furthermore, we show that the necessary lookahead to win a deterministic context-free delay game can...

It is shown how weighted context-free grammars can be used to recognize languages beyond their weak generative capacity by a one-step constant time extension of standard recognition algorithms.

In a recent paper (M. Barash, A. Okhotin, “An extension of context-free grammars with one-sided context specifications”, Inform. Comput., 2014), the authors introduced an extension of the context-free grammars equipped with an operator for referring to the left context of the substring being defined. This paper proposes a more general model, in which context specifications may be two-sided, tha...

The close relationship between Petri nets and language theory has been extensively studied for a long time [1, 2]. Results from the theory of Petri nets have been applied successfully to provide elegant solutions to complicated problems from language theory [4, 7]. A context-free grammar can be associated with a context-free (communica-tion-free) Petri net, whose places and transitions, corresp...

We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an assumption that the terminal alphabet is fixed, the membership problem for regular grammars (given v in binary and a regular commutative grammar G, does G generate v...

Divide the context-free languages into equivalence classes in the following way: L1 and L2 are in the same class if there are a-transducers M and M such that M(L1) ~ L~ and d~r(L,) = L1. Define L1 and L~ to be structurally similar if they are in the same class. Among the results given below are: (I) if L1 and L2 are structurally similar and L1 has a structurally similar set of (right) sententia...

A test set for a formal language (set of strings) L is a subset T of L such that for any two string homomorphisms f and g defined on L, if the restrictions of f and g on T are identical functions, then f and g are identical on the entire L. Previously, it was shown that there are context-free grammars for which smallest test sets are cubic in the size of the grammar, which gives a lower bound o...

A context-free grammar G (henceforth abbreviated to “grammar”) is a 4-tuple (N,V, P, S) consisting of the following components: a finite set N of non-terminal variables, a finite set V of terminal variables that is disjoint from N , a finite set P of production rules, mapping non-terminal variables to a series of non-terminals and terminals, and a distinguished symbol S ∈ N that is the start sy...

We present two structural results concerning longest common prefixes of non-empty languages. First, we show that the longest common prefix of the language generated by a context-free grammar of size N equals the longest common prefix of the same grammar where the heights of the derivation trees are bounded by 4N . Second, we show that each non-empty language L has a representative subset of at ...