Showing papers on "Recursively enumerable language published in 2004"
31 Aug 2004
TL;DR: The modal fixed point logic (HFL) as mentioned in this paper extends the modal μ-calculus to allow predicates on states (sets of states) to be specified using recursively defined higher order functions on predicates.
Abstract: We present a higher order modal fixed point logic (HFL) that extends the modal μ-calculus to allow predicates on states (sets of states) to be specified using recursively defined higher order functions on predicates. The logic HFL includes negation as a first-class construct and uses a simple type system to identify the monotonic functions on which the application of fixed point operators is semantically meaningful. The model checking problem for HFL over finite transition systems remains decidable, but its expressiveness is rich. We construct a property of finite transition systems that is not expressible in the Fixed Point Logic with Chop [1] but which can be expressed in HFL. Over infinite transition systems, HFL can express bisimulation and simulation of push down automata, and any recursively enumerable property of a class of transition systems representing the natural numbers.
56 citations
TL;DR: It is shown that many NP-complete problems can be solved in linear time in a quite uniform way (by systems which are very similar to each other), using only elementary membranes division (and not further ingredients, such as electrical charges).
55 citations
TL;DR: It is shown that 1-region membrane computing systems which only use rules of the form Ca → Cv are equivalent to communication-free Petri nets, which are also equivalent to commutative context-free grammars, and that systems of the first type define precisely the semilinear sets.
47 citations
04 Jul 2004
13 Dec 2004
TL;DR: This paper makes the expanding domain assumption, that is, D n ⊆ D m if n
Abstract: First-Order Temporal Logic, FOTL, is an extension of classical first-order logic by temporal operators for a discrete linear model of time (isomorphic to ℕ, that is, the most commonly used model of time). Formulae of this logic are interpreted over structures that associate with each element n of ℕ, representing a moment in time, a first-order structure (D n ,I n ) with its own non-empty domain D n . In this paper we make the expanding domain assumption, that is, D n ⊆ D m if n
45 citations
01 Dec 2004
TL;DR: A higher order modal fixed point logic (HFL) that extends the modal μ-calculus to allow predicates on states (sets of states) to be specified using recursively defined higher order functions on predicates.
Abstract: We present a higher order modal fixed point logic (HFL) that extends the modal μ-calculus to allow predicates on states (sets of states) to be specified using recursively defined higher order functions on predicates. The logic HFL includes negation as a first-class construct and uses a simple type system to identify the monotonic functions on which the application of fixed point operators is semantically meaningful. The model checking problem for HFL over finite transition systems remains decidable, but its expressiveness is rich. We construct a property of finite transition systems that is not expressible in the Fixed Point Logic with Chop [1] but which can be expressed in HFL. Over infinite transition systems, HFL can express bisimulation and simulation of push down automata, and any recursively enumerable property of a class of transition systems representing the natural numbers.
41 citations
TL;DR: This paper gives exact recursion-theoretical characterization of the computational power of this kind of fuzzy Turing machines and shows that fuzzy languages accepted by these machines with a computable t-norm correspond exactly to the union Σ10 ∪ Π10 of recursively enumerable languages and their complements.
39 citations
14 Jun 2004
TL;DR: It is proved that two classes of communicative P systems with 3 membranes and with minimal cooperation are computationally complete: they generate all recursively enumerable sets of vectors of nonnegative integers.
Abstract: We prove that two classes of communicative P systems with 3 membranes and with minimal cooperation, namely P systems with symport/antiport rules of size 1 and and P systems with symport rules of size 2, are computationally complete: they generate all recursively enumerable sets of vectors of nonnegative integers. The result of computation is obtained in the elementary membrane.
37 citations
TL;DR: It is proved that recursively enumerable languages can be generated by matrix grammars with only two non-terminal symbols being used in the appearance checking mode, and three classes of membrane systems are considered, and in all the three cases the hierarchies are shown to collapse at level four.
35 citations
TL;DR: P/O systems are introduced to generate any recursively enumerable language and a class of languages between the context-free and context-sensitive ones is obtained.
32 citations
01 Jan 2004
TL;DR: Alhazov et al. as mentioned in this paper introduced P/O systems to generate any recursively enumerable language, and obtained a class of languages between the context-free and context-sensitive ones.
Abstract: In biology and chemistry a standard proceeding is to conduct an experiment, observe its progress, andthen take the result of this observation as the 1nal output. Inspiredby this, we have introduced P/O systems (A. Alhazov, C. Mart5 6n-Vide, Gh. P9 aun, Pre-Proc. of the Workshop on Membrane Computing 2003, Tarrragona, Spain; http://pizarro. ces to generate any recursively enumerable language. In a thirdcase, we obtain a class of languages between the context-free andcontext-sensitive ones. c 2004 Elsevier B.V. All rights reserved.
28 citations
TL;DR: A complete characterization is given for the Boolean hierarchy of partitions over some important lattices, in particular, over the lattices of recursively enumerable sets and of open sets in the Baire space.
Abstract: The Boolean hierarchy of partitions was introduced and studied by Kosub and Wagner, primarily over the lattice of NP-sets. Here, this hierarchy is treated over lattices with the reduction property, showing that it has a much simpler structure in this instance. A complete characterization is given for the hierarchy over some important lattices, in particular, over the lattices of recursively enumerable sets and of open sets in the Baire space.
TL;DR: The generative capability of several variants of P systems with symport/antiport is studied via the simulation of counter automata, leading to the reduction of the complexity, expressed in number of membranes and weight of rules, of P system generating recursively enumerable sets.
Abstract: The generative capability of several variants of P systems with symport/antiport is studied via the simulation of counter automata. This leads to the reduction of the complexity, expressed in number of membranes and weight of rules, of P systems generating recursively enumerable sets.
21 Sep 2004
TL;DR: This paper provides a geometric model of computation, conservative abstract geometrical computation, that, although being based on rational numbers, has the same property: it can simulate any Turing machine and can decide any recursively enumerable problem through the creation of an accumulation.
Abstract: The Black hole model of computation provides super-Turing computing power since it offers the possibility to decide in finite (observer's) time any recursively enumerable ($\mathcal{R.E.}$) problem. In this paper, we provide a geometric model of computation, conservative abstract geometrical computation, that, although being based on rational numbers, has the same property: it can simulate any Turing machine and can decide any $\mathcal{R.E.}$ problem through the creation of an accumulation. Finitely many signals can leave any accumulation, and it can be known whether anything leaves. This corresponds to a black hole effect.
TL;DR: It is shown that the set of fixed-point combinators forms a recursively-enumerable subset of a larger set of terms that is not Recursively enumerable, and the terms of which are observationally equivalent to fixed- point combinators in any computable context.
Abstract: We show that the set of fixed-point combinators forms a recursively-enumerable subset of a larger set of terms that is (A) not recursively enumerable, and (B) the terms of which are observationally equivalent to fixed-point combinators in any computable context.
Proceedings Article•
01 Jan 2004
TL;DR: A geometric model of computation, conservative abstract geo- metrical computation, that, although being based on rational numbers, has the same property: it can simulate any Turing machine and can de- cide any R.E. problem through the creation of an accumulation.
Abstract: The Black hole model of computation provides super-Turing computing power since it offers the possibility to decide in finite (ob- server's) time any recursively enumerable (R.E.) problem. In this paper, we provide a geometric model of computation, conservative abstract geo- metrical computation, that, although being based on rational numbers, has the same property: it can simulate any Turing machine and can de- cide any R.E. problem through the creation of an accumulation. Finitely many signals can leave any accumulation, and it can be known whether anything leaves. This corresponds to a black hole effect.
TL;DR: It is shown that the Turing degree structure of the orbits of these automata is the same as for general cellular automata, especially those whose orbits have arbitrary recursively enumerable degree.
TL;DR: A definition of an extended system is given, and its universality is proved using the rules of more restricted types, and it is proved that 2-membrane EC P automata with a promoter can accept all recursively enumerable languages.
Abstract: Evolution-communication P systems are a variant of P systems allowing both rewriting rules and symport/antiport rules, thus having separated the rewriting and the communication. The purpose of this paper is to solve an open problem stated in Reference [1], namely generating the family of Turing computable sets of vectors of natural numbers instead of the family of Turing computable sets of natural numbers. The same construction also reduces the 3-membrane non-cooperative case and the 2-membrane 1-catalyst case to the 2-membrane non-cooperative case. Also, EC P automata are introduced and it is proved that 2-membrane EC P automata with a promoter can accept all recursively enumerable languages. Finally, a definition of an extended system is given, and its universality is proved using the rules of more restricted types.
14 Jun 2004
TL;DR: Each recursively enumerable tree language can be obtained in that way generated by P systems with active membranes working on strings by considering the resulting tree representing the membrane structure of the final configuration.
Abstract: We consider P systems with active membranes, but without polarizations, yet with using membrane division and membrane generation, but as the result of a halting computation we do not take the terminal string generated in a designated output membrane, instead we consider the resulting tree representing the membrane structure of the final configuration as its result. We show that each recursively enumerable tree language can be obtained in that way generated by P systems with active membranes working on strings.
TL;DR: In this article, a new type of shift dynamics is introduced, called functional shift, which is defined by a set of bi-infinite sequences of some functions on a given set of symbols.
Abstract: We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift, which is defined by a set of bi-infinite sequences of some functions on a set of symbols. To analyse the complexity of functional shifts, we measure them in terms of topological entropy, and locate their languages in the Chomsky hierarchy. Through this study, we argue that considering functional shifts from the viewpoints of both dynamics and computation gives us opposite results about the complexity of systems. We also describe a new class of shift spaces whose languages are not recursively enumerable.
Journal Article•
Metz1
TL;DR: In this article, it was shown that a tissue P system with 3 cells and 2 symport/antiport rules of minimal weight can generate all recursively enumerable sets of numbers.
Abstract: We show that tissue P systems with symport/antiport having 3 cells and symport/antiport rules of minimal weight generate all recursively enumerable sets of numbers. Constructed systems simulate register machines and have purely deterministic behaviour. Moreover, only 2 symport rules are used and all symbols of any system are present in finite number of copies (except for symbols corresponding to registers of the machine). At the end of the article some open problems are formulated.
Journal Article•
TL;DR: This paper proves that every non-unary recursively enumerable language is defined by a centralized two-way grammar system, Γ, with two metalinear components in a very economical way.
Abstract: Besides a derivation step and a communication step, a two-way PC grammar system can make a reduction step during which it reduces the right-hand side of a context-free production to its left hand-side. This paper proves that every non-unary recursively enumerable language is defined by a centralized two-way grammar system, Γ, with two metalinear components in a very economical way. Indeed, Γ's master has only three nonterminals and one communication production; furthermore, it produces all sentential forms with no more than two occurrences of nonterminals. In addition, during every computation, Γ makes a single communication step. Some variants of two-way PC grammar systems are discussed in the conclusion of this paper.
21 Sep 2004
TL;DR: In this paper, the authors consider evolution/observation as a new strategy also for accepting languages: a word is accepted, if the (observed) evolution of a certain system starting from this input follows a regular pattern.
Abstract: It is a very common procedure in biology to observe the progress of an experiment and regard the result of this observation as the final outcome. Inspired by this, a new approach for generating formal languages, called evolution/observation, has been introduced [6]. In the current work we consider evolution/observation as a new strategy also for accepting languages: a word is accepted, if the (observed) evolution of a certain system starting from this input follows a regular pattern.
We obtain the following result: checking if the (observed) evolution of a context-free system follows a regular pattern is enough to accept every recursively enumerable languages. On the other hand, if we observe the evolution of systems using very simple rules (of the kind a → b), then it is possible to accept exactly the class of context-sensitive languages.
TL;DR: This work considers P systems with active membranes, allowing membrane creation or division or duplication and dissolution, where the output of a computation may be obtained either by visiting the tree associated with the membrane structure, or by following the traces of a specific object.
Abstract: We propose an alternative approach to generate languages by means of P systems: building up an appropriate representation for a string by means of a corresponding membrane structure and then generating the string by visiting the membrane structure according to a well-specified strategy To this aim, we consider P systems with active membranes, allowing membrane creation or division or duplication and dissolution, where the output of a computation may be obtained either by visiting the tree associated with the membrane structure, or by following the traces of a specific object, called traveller, or sending out the objects For each of these approaches, we provide characterizations of reeursively enumerable languages based on P systems that use different sets of operations for modifying the membrane structure
01 Jan 2004
TL;DR: In this paper, it was shown that four membranes suffice to generate all recursively enumerable sets of numbers with maximal parallelism in P systems with symport/antiport.
Abstract: It is proved that four membranes suffice to a variant of P systems with symport/antiport with maximal parallelism to generate all recursively enumerable sets of numbers. P systems with symport/antiport without maximal parallelism are also studied, considering two termination criteria.
Metz1
TL;DR: It is shown that tissue P systems with symports having 3 cells and symport/antiport rules of minimal weight generate all recursively enumerable sets of numbers.
Abstract: We show that tissue P systems with symport/antiport having 3 cells and symport/antiport rules of minimal weight generate all recursively enumerable sets of numbers. Constructed systems simulate register machines and have purely deterministic behaviour. Moreover, only 2 symport rules are used and all symbols of any system are present in finite number of copies (except for symbols corresponding to registers of the machine). At the end of the article some open problems are formulated.
TL;DR: For I=Ex, it is shown that only consistently learnable classes can be uniformly robustly learnable and the first results on separating robust learning from uniformly robust learning are derived.
13 Dec 2004
TL;DR: In this article, the only remaining step in the Chomsky hierarchy is to consider those groups with a context-sensitive word problem and prove some results about these groups, and also establish some results for other context sensitive decision problems in groups.
Abstract: There already exist classifications of those groups which have regular, context-free or recursively enumerable word problem. The only remaining step in the Chomsky hierarchy is to consider those groups with a context-sensitive word problem. In this paper we consider this problem and prove some results about these groups. We also establish some results about other context-sensitive decision problems in groups.
01 Jan 2004
TL;DR: The aim of this paper is to try to merge a notion of activator a formal model of enzyme as a usual symbolobject, more or less a middle notion between a catalyst and a promoter.
Abstract: The usual assumption in P systems behavior is that of maximal parallelism, however in living cells it is not the case because they have a limited number of enzymes. The aim of this paper is to try to merge these ideas by introducing a notion of activator a formal model of enzyme as a usual symbolobject, more or less a middle notion between a catalyst and a promoter. Each activator executes one (context-free) rule, and can evolve in the same step. The rules will need activators to be applied, so the parallelism of each rule is maximal, but limited to the number of its activators. Such systems can generate any recursively enumerable language or deterministically accept any recursively enumerable set of vectors of nonnegative integers. It is open what is the power of P systems with uniport rules and activators.
TL;DR: It is proved that this problem of deciding the existence of codings between trace monoids is not recursively enumerable, and its decidability is shown when restricted to instances with domain monoids defined by acyclic dependence graphs.
Journal Article•
TL;DR: Several characterizations of the family of the recursively enumerable lan- guages based on matrix grammars with conditions of a limited length, a reduced number of nonterminals, and a re- duced number and size of matrices are established.
Abstract: This paper discusses some conditional versions of matrix grammars. It establishes several characterizations of the family of the recursively enumerable lan- guages based on these grammars. In fact, making use of the Geffert Normal forms, the present paper demonstrates these characterizations based on matrix grammars with conditions of a limited length, a reduced number of nonterminals, and a re- duced number and size of matrices.