scholarly journals Adding Matrix Control: Insertion-Deletion Systems with Substitutions III

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 131
Author(s):  
Martin Vu ◽  
Henning Fernau
Keyword(s):  
Turing Machines ◽  
Biological Mechanisms ◽  
Computational Completeness ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
The Family ◽  
Short Program ◽  
Matrix Control ◽  
Recursively Enumerable Languages

Insertion-deletion systems have been introduced as a formalism to model operations that find their counterparts in ideas of bio-computing, more specifically, when using DNA or RNA strings and biological mechanisms that work on these strings. So-called matrix control has been introduced to insertion-deletion systems in order to enable writing short program fragments. We discuss substitutions as a further type of operation, added to matrix insertion-deletion systems. For such systems, we additionally discuss the effect of appearance checking. This way, we obtain new characterizations of the family of context-sensitive and the family of recursively enumerable languages. Not much context is needed for systems with appearance checking to reach computational completeness. This also suggests that bio-computers may run rather traditionally written programs, as our simulations also show how Turing machines, like any other computational device, can be simulated by certain matrix insertion-deletion-substitution systems.

Jumping Grammars

2015 ◽  
Vol 26 (06) ◽  
pp. 709-731 ◽  
Author(s):  
Zbyněk Křivka ◽  
Alexander Meduna
Keyword(s):  
Finite Index ◽  
Open Problems ◽  
Generative Power ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
The Family ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

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.

CD GRAMMAR SYSTEMS WITH REGULAR START CONDITIONS

2008 ◽  
Vol 19 (04) ◽  
pp. 767-779
Author(s):  
RUDOLF FREUND ◽  
MARION OSWALD
Keyword(s):  
Finite Index ◽  
Hybrid Mode ◽  
Computational Completeness ◽  
Recursively Enumerable ◽  
The Family ◽  
Grammar Systems ◽  
Regular Sets ◽  
Classical Derivation ◽  
Recursively Enumerable Languages

We consider cooperating distributed grammar systems with the components working in different derivation modes as well as with regular sets as additional start conditions for the components. With the classical derivation modes ≤ k and = k as well as with the internally hybrid mode (≥ ℓ∧ ≤ k) we obtain a characterization of the family of recursively enumerable languages even with only one component, with the derivation modes *, t, and ≥ k as well as with the internally hybrid mode (t∧ ≥ k) two components working in the same mode and only one common regular set for both components yield computational completeness. For the internally hybrid modes (t∧ ≤ k) and (t∧ = k) we only obtain languages of finite index, but combining one component working in one of these modes (t∧ ≤ k) and (t∧ = k) with a component working in one of the modes * and ≥ k we again obtain a characterization of the family of recursively enumerable languages.

scholarly journals Derivation "Trees" and Parallelism in Chomsky-Type Grammars

Triangle ◽  
2018 ◽  
pp. 101
Author(s):  
Benedek Nagy
Keyword(s):  
Formal Language ◽  
Phrase Structure ◽  
Formal Language Theory ◽  
Language Theory ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
Rule Set ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

In this paper we discuss parallel derivations for context-free, contextsensitive and phrase-structure grammars. For regular and linear grammars only sequential derivation can be applied, but a kind of parallelism is present in linear grammars. We show that nite languages can be generated by a recursion-free rule-set. It is well-known that in context-free grammars the derivation can be in maximal (independent) parallel way. We show that in cases of context-sensitive and recursively enumerable languages the parallel branches of the derivation have some synchronization points. In the case of context-sensitive grammars this synchronization can only be local, but in a derivation of an arbitrary grammar we cannot make this restriction. We present a framework to show how the concept of parallelism can be t to the derivations in formal language theory using tokens.

PROBABILISTIC REWRITING P SYSTEMS

2003 ◽  
Vol 14 (01) ◽  
pp. 157-166 ◽  
Author(s):  
MUTYAM MADHU
Keyword(s):  
P Systems ◽  
Cut Point ◽  
Recursively Enumerable ◽  
The Family ◽  
Rewriting Rules ◽  
Recursively Enumerable Languages ◽  
Selection Of

In this paper we define a variant of P systems, namely, probabilistic rewriting P systems, where the selection of rewriting rules is probabilistic. We show that, with non-zero cut-point, probabilistic rewriting P systems with/without priorities generate only finite languages, but with zero cut/point and without priorities, probabilistic rewriting P systems of degree 1 characterize the family of languages generated by matrix grammars. We also prove that probabilistic rewriting P systems of degree 1 with zero cut-point and priorities characterize recursively enumerable languages.

ON THE POWER OF ONE-WAY SYNCHRONIZED ALTERNATING MACHINES WITH SMALL SPACE

1992 ◽  
Vol 03 (01) ◽  
pp. 65-79 ◽  
Author(s):  
JURAJ HROMKOVIČ ◽  
KATSUSHI INOUE ◽  
BRANISLAV ROVAN ◽  
ANNA SLOBODOVÁ ◽  
ITSUO TAKANAMI ◽  
...  
Keyword(s):  
Finite Automata ◽  
Turing Machines ◽  
Small Space ◽  
Closure Properties ◽  
Open Problems ◽  
Infinite Hierarchy ◽  
Context Sensitive ◽  
The Family

This paper continues the investigation of the concept of synchronized alternation. The open problems from Ref. 4 are solved by showing that one-way synchronized alternating (multihead) automata are as powerful as two-way ones. More precisely it is shown that: (i) one-way synchronized alternating finite automata recognize exactly context-sensitive languages, and (ii) NSPACE(nk) is exactly the family of languages recognized by one-way (two-way) synchronized alternating k-head finite automata, for k≥1. Finaly, the synchronization complexity of one-way synchronized Turing machines (1satm's) is investigated and an infinite hierarchy among classes of sets accepted by 1satm's with space and synchronization bounds between log log n and log n is established. Some closure properties of the classes in this hierarchy are also proved.

scholarly journals Separating the Classes of Recursively Enumerable Languages Based on Machine Size

2015 ◽  
Vol 26 (06) ◽  
pp. 677-695
Author(s):  
Jan van Leeuwen ◽  
Jiří Wiedermann
Keyword(s):  
Nineteen Sixties ◽  
Turing Machines ◽  
Recursively Enumerable ◽  
Language L ◽  
Finite Language ◽  
Recursively Enumerable Languages

In the late nineteen sixties it was observed that the r.e. languages form an infinite proper hierarchy [Formula: see text] based on the size of the Turing machines that accept them. We examine the fundamental position of the finite languages and their complements in the hierarchy. We show that for every finite language L one has that L, [Formula: see text] for some [Formula: see text] where m is the length of the longest word in L, c is the cardinality of L, and [Formula: see text]. If [Formula: see text], then [Formula: see text] for some [Formula: see text]. We also prove that for every n, there is a finite language Ln with [Formula: see text] such that [Formula: see text] but Ln, [Formula: see text] for some [Formula: see text]. Several further results are shown that how the hierarchy can be separated by increasing chains of finite languages. The proofs make use of several auxiliary results for Turing machines with advice.

PARALLEL FINITE AUTOMATA SYSTEMS COMMUNICATING BY STATES

2002 ◽  
Vol 13 (05) ◽  
pp. 733-749 ◽  
Author(s):  
CARLOS MARTÍN-VIDE ◽  
ALEXANDRU MATEESCU ◽  
VICTOR MITRANA
Keyword(s):  
Finite Automata ◽  
Point Of View ◽  
Computational Power ◽  
Open Problems ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
Power Point ◽  
Grammar Systems ◽  
Recursively Enumerable Languages ◽  
Parallel Communicating Grammar Systems

An accepting device based on the communication between finite automata working in parallel is introduced. It consists of several finite automata working independently but communicating states to each other by request. Several variants of parallel communicating finite automata systems are investigated from their computational power point of view. We prove that all of them are at most as powerful as multi-head finite automata. Homomorphical characterizations of recursively enumerable languages are obtained starting from languages recognized by all variants of parallel communicating finite automata systems having at most three components. We present a brief comparison with the parallel communicating grammar systems. Some remarks suggesting that these devices might be mildly context-sensitive ones as well as a few open problems and directions for further research are also discussed.

Sign in / Sign up

Export Citation Format

Share Document