This paper introduces and studies jumping grammars, which represent a grammatical counterpart to the recently introduced jumping automata. These grammars are conceptualized just like classical grammars except that during the applications of their productions, they can jump over symbols in either direction within the rewritten strings. More precisely, a jumping grammar rewrites a string z according to a rule x → y in such a way that it selects an occurrence of x in z, erases it, and inserts y anywhere in the rewritten string, so this insertion may occur at a different position than the erasure of x.The paper concentrates its attention on investigating the generative power of jumping grammars. More specifically, it compares this power with that of jumping automata and that of classical grammars. A special attention is paid to various context-free versions of jumping grammars, such as regular, right-linear, linear, and context-free grammars of finite index. In addition, we study the semilinearity of context-free, context-sensitive, and monotonous jumping grammars. We also demonstrate that the general versions of jumping grammars characterize the family of recursively enumerable languages. In its conclusion, the paper formulates several open problems and suggests future investigation areas.Processing information in a largely discontinuous way represents a common computational phenomenon today [1,2,8]. Indeed, consider a process p that deals with information i. During a single computational step, p can read a piece of information x in i, erase it, generate a new piece of information y, and insert y into i possibly far away from the original 709 Int. J. Found. Comput. Sci. 2015.26:709-731. Downloaded from www.worldscientific.com by WEIZMANN INSTITUTE OF SCIENCE on 12/31/15. For personal use only.
The present paper modifies and studies jumping finite automata so they always perform two simultaneous jumps according to the same rule. For either of the two simultaneous jumps, it considers three natural directions – (1) to the left, (2) to the right, and (3) in either direction. According to this jumping-direction three-part classification, the paper investigates the mutual relation between the language families resulting from jumping finite automata performing the jumps in these ways and the families of regular, linear, context-free, and context-sensitive languages. It demonstrates that most of these language families are pairwise incomparable. In addition, many closure and non-closure properties of the resulting language families are established.
This paper introduces and discusses ^-rewriting systems, which represent languagegenerating devices that resemble automata by using finitely many states without any nonterminals. It demonstrates that these systems characterize the well-known infinite hierarchy of language families resulting from programmed grammars of finite index in a very natural way. In its conclusion, this paper suggests some variants of #-rewriting systems.
In this paper, we discuss cooperating distributed grammar systems where components are (variants of) random context grammars. We give an overview of known results and open problems, and prove some further results.
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