Topic
Recursively enumerable language
About: Recursively enumerable language is a research topic. Over the lifetime, 1508 publications have been published within this topic receiving 32382 citations.
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25 Sep 1999
TL;DR: In this article, it was shown that recursive Petri nets (RPNs) are recursive and that any recursively enumerable language may be obtained as the image by an homomorphism of the intersection of a regular language and a RPN language.
Abstract: Recursive Petri nets (RPNs) have been introduced to model systems with dynamic structure. Whereas this model is a strict extension of Petri nets, reachability in RPNs remains decidable. Here we focus on three complementary theoretical aspects. At first, we develop decision procedures for new properties like boundedness and finiteness and we show that languages of RPNs are recursive. Then we study the expressiveness of RPNs proving that any recursively enumerable language may be obtained as the image by an homomorphism of the intersection of a regular language and a RPN language. Starting from this property, we deduce undecidability results including undecidablity for the kind of model checking which is decidable for Petri nets. At last, we compare RPNs with two other models combining Petri nets and context-free grammars features showing that these models can be simulated by RPNs.
8 citations
Proceedings Article•
01 Jan 1998TL;DR: It is proved that the paper extends some of the most recently obtained results on the computational universality of specific variants of H systems and proves that it can construct universal computers based on various types of H system with a finite set of splicing rules as well as a finiteSet of axioms.
Abstract: First, we recall some characterizations of recursively enumerable languages by means of finite H systems with certain regulations on the splicing operation. Then, we consider a variant of the splicing operation where the splicing proceeds always in couples of steps: the two strings obtained after a splicing enter immediately a second splicing (the rules used in the two steps are not prescribed). Somewhat surprising if we take into account the loose control on the performed operations, extended H systems with finite sets of axioms and of splicing rules, using this double splicing operation, can again characterize the recursively enumerable languages. Finally, we consider two types of distributed H systems: communicating distributed H systems and time-varying distributed H systems. For the first type of devices, we give a new proof of the recent result of [25] that (in the extended case) such systems with three components characterize the recursively enumerable languages. In what concerns the second mentioned distributed model, we prove that time-varying H systems with seven components can characterize the recursively enumerable languages. The optimality of these two last-mentioned results is open.
8 citations
TL;DR: This paper presents two results, both of which strengthen the general conclusion that repeat is a stronger construct than loop, in several respects, and shows that QDL, the first-order version of dynamic logic, is more expressive with repeat than with loop.
8 citations
19 Jun 1989
TL;DR: In this paper, it was shown that for recursively enumerable sets, p-creativeness and p-complete creativeness are equivalent, and Myhill's theorem still holds in the polynomial setting.
Abstract: It is shown that for recursively enumerable sets, p-creativeness and p-complete creativeness are equivalent, and Myhill's theorem still holds in the polynomial setting. For P (NP), p-creativeness is shown to be equivalent to p-complete creativeness. The existence of p-creative sets for P (NP) in EXP (NEXP) is given. Moreover, it is shown that every p-m-complete set for EXP (NEXP) is p-completely creative for P (NP), and every p-creative set for NP is NP-hard via many-one reductions. Other results for k-completely creative sets are obtained. >
8 citations
TL;DR: In this article, it was shown that the equational/order theory of a model of the untyped λ-calculus can not be recursively enumerable.
Abstract: A longstanding open problem is whether there exists a non-syntactical model of the untyped λ-calculus whose theory is exactly the least λ-theory λβ In this paper we investigate the more general question of whether the equational/order theory of a model of the untyped λ-calculus can be recursively enumerable (re for short) We introduce a notion of effective model of λ-calculus, which covers, in particular, all the models individually introduced in the literature We prove that the order theory of an effective model is never re; from this it follows that its equational theory cannot be λβ or λβη We then show that no effective model living in the stable or strongly stable semantics has an re equational theory For Scott's semantics, we investigate the class of graph models and prove that no order theory of a graph model can be re, and that there exists an effective graph model whose equational/order theory is the minimum among the theories of graph models Finally, we show that the class of graph models enjoys a kind of downwards Lowenheim–Skolem theorem
8 citations