Language Acceptors Research Articles

Weak Muller acceptance conditions for tree automata

Over the last decades the theory of automata on infinite objects has been an important source of tools for the specification and the verification of computer programs. Trees are more suitable than words to model nondeterminism and concurrency. In the literature, there are several examples of acceptance conditions that have been proposed for automata on infinite words and then have been fruitfully extended to infinite trees. The type of acceptance condition can influence both the succinctness of the language acceptors and the computational complexity of the decision problems. Here we consider, relatively to automata on infinite trees, two acceptance conditions that are obtained by a relaxation of the Muller acceptance condition: the Landweber and the Muller-Superset conditions. We prove that Muller-Superset tree automata accept the same class of languages as Büchi tree automata. Also, we show that for such languages the minimal Muller-Superset acceptor is at least as succinct as the minimal Büchi acceptor and, in some cases, it can be exponentially more succinct. Landweber tree automata, instead, define a class of languages that is not comparable with that defined by Büchi tree automata. The main result we prove is that the emptiness problem for this class of automata is decidable in polynomial time, and thus we extend the class of automata with a tractable emptiness problem.

On membrane hierarchy in P systems

We look at a restricted model of a communicating P system, called RCPS, whose environment does not contain any object initially. The system can expel objects into the environment but only expelled objects can be retrieved from the environment. Such a system is initially given an input a 1 i 1 … a n i n (with each i j representing the multiplicity of distinguished object a i , 1 ⩽ i ⩽ n ) and is used as an acceptor. We show that RCPSs are equivalent to two-way multihead finite automata over bounded languages (i.e., subsets of a 1 * … a n * , for some distinct symbols a 1 , … , a n ). We then show that there is an infinite hierarchy of RCPS's in terms of the number of membranes: For every r , there is an s > r and a unary language L accepted by an RCPS with s membranes that cannot be accepted by an RCPS with r membranes. This provides an answer to an open problem in (Membrane Computing: An Introduction, Springer, Berlin, 2002) which asks whether there is a nonuniversal model of a membrane computing system which induces an infinite hierarchy on the number of membranes. We also consider variants/generalizations of RCPSs, e.g, acceptors of languages; models that allow a “polynomial bounded” supply of objects in the environment initially; models with tentacles, etc. We show that they also form an infinite hierarchy with respect to the number of membranes (or tentacles). The proof techniques can be used to obtain similar results for other restricted models of P systems, like symport/antiport systems.

Fast one-way cellular automata

Space-bounded one-way cellular language acceptors (OCA) are investigated. The only inclusion known to be strict in their time hierarchy from real-time to exponential-time is between real-time and linear-time! We show the surprising result that there exists an infinite hierarchy of properly included OCA-language families in that range. A generalization of a method in Terrier (Theoret. Comput. Sci. 156 (1–2) (1996) 281) is shown which provides a tool for proving that languages are not acceptable by OCAs with small time bounds. The hierarchies are established by such a language and a translation result. In addition, a notion of constructibility for CAs is introduced, along with some of its properties. We prove several closure properties of the families in the hierarchy.

A systolic design for acceptors of regular languages

In this paper we present a derivation method for networks of systolic cells. The method is calculational and can be applied for specifications that are data-independent, i.e. the order of communications does not depend on the values communicated. The techniques used in this style of parallel programming are comparable with techniques used in sequential programming. The presentation is done by means of an example: the derivation of a set of building blocks for the construction of acceptors for regular languages.

Fast language acceptance by shrinking cellular automata

When bounded cellular automata are used as acceptors for formal languages, the number of time steps required to accept a string σ is at least ¦σ¦, except in certain trivial cases, since the distinguished cell's state after t steps cannot depend on the initial states of the cells at distances > t from it. However, if the automaton is allowed to shrink (i.e., cells are deleted, and their predecessors become directly connected to their successors), language acceptance in less than linear time becomes possible.

Realization of A/D and D/A coders

Abstract : The notion of a discrete-time coder as a device which converts real vector-valued sequences into sequences over a finite alphabet is formalized. A hierarchical classification of all coders, in terms of their input-output mappings, is sought. This classification is based on a canonical structure theory being developed for coders. An algebraic approach is used to define three classes of coders which have simple canonical realizations, i.e., ones for which known synthesis procedures may be used. It is proposed that coders be viewed as acceptors of real languages, and the hierarchy of the real languages be used in conjunction with the hierarchy suggested by these three coders to achieve a complete classification. (Author)

A Class of Push-Down Acceptors for Adjunct Languages

The local adjunct languages (LAL's) and grammars have been defined so as to characterize many aspects of natural and programming languages.