205,619 research outputs found
Groups with poly-context-free word problem
We consider the class of groups whose word problem is poly-context-free; that
is, an intersection of finitely many context-free languages. We show that any
group which is virtually a finitely generated subgroup of a direct product of
free groups has poly-context-free word problem, and conjecture that the
converse also holds. We prove our conjecture for several classes of soluble
groups, including metabelian groups and torsion-free soluble groups, and
present progress towards resolving the conjecture for soluble groups in
general. Some of the techniques introduced for proving languages not to be
poly-context-free may be of independent interest.Comment: 38 pages, no figure
Type Classes for Lightweight Substructural Types
Linear and substructural types are powerful tools, but adding them to
standard functional programming languages often means introducing extra
annotations and typing machinery. We propose a lightweight substructural type
system design that recasts the structural rules of weakening and contraction as
type classes; we demonstrate this design in a prototype language, Clamp.
Clamp supports polymorphic substructural types as well as an expressive
system of mutable references. At the same time, it adds little additional
overhead to a standard Damas-Hindley-Milner type system enriched with type
classes. We have established type safety for the core model and implemented a
type checker with type inference in Haskell.Comment: In Proceedings LINEARITY 2014, arXiv:1502.0441
Tree transducers, L systems, and two-way machines
A relationship between parallel rewriting systems and two-way machines is investigated. Restrictions on the “copying power” of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying. Among the parallel rewriting systems considered are the top-down tree transducer; the generalized syntax-directed translation scheme and the ETOL system, and among the two-way machines are the tree-walking automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton. The. relationship of these devices to macro grammars is also considered. An effort is made .to provide a systematic survey of a number of existing results
On the Properties of Language Classes Defined by Bounded Reaction Automata
Reaction automata are a formal model that has been introduced to investigate
the computing powers of interactive behaviors of biochemical reactions([14]).
Reaction automata are language acceptors with multiset rewriting mechanism
whose basic frameworks are based on reaction systems introduced in [4]. In this
paper we continue the investigation of reaction automata with a focus on the
formal language theoretic properties of subclasses of reaction automata, called
linearbounded reaction automata (LRAs) and exponentially-bounded reaction
automata (ERAs). Besides LRAs, we newly introduce an extended model (denoted by
lambda-LRAs) by allowing lambda-moves in the accepting process of reaction, and
investigate the closure properties of language classes accepted by both LRAs
and lambda-LRAs. Further, we establish new relationships of language classes
accepted by LRAs and by ERAs with the Chomsky hierarchy. The main results
include the following : (i) the class of languages accepted by lambda-LRAs
forms an AFL with additional closure properties, (ii) any recursively
enumerable language can be expressed as a homomorphic image of a language
accepted by an LRA, (iii) the class of languages accepted by ERAs coincides
with the class of context-sensitive languages.Comment: 23 pages with 3 figure
Extended macro grammars and stack controlled machines
K-extended basic macro grammars are introduced, where K is any class of languages. The class B(K) of languages generated by such grammars is investigated, together with the class LB(K) of languages generated by the corresponding linear basic grammars. For any full semi-AFL K, B(K) is a full AFL closed under iterated LB(K)-substitution, but not necessarily under substitution. For any machine type D, the stack controlled machine type corresponding to D is introduced, denoted S(D), and the checking-stack controlled machine type CS(D). The data structure of this machine is a stack which controls a pushdown of data structures from D. If D accepts K, then S(D) accepts B(K) and CS(D) accepts LB(K). Thus the classes B(K) are characterized by stack controlled machines and the classes LB(K), i.e., the full hyper-AFLs, by checking-stack controlled machines. A full basic-AFL is a full AFL K such that B(K)C K. Every full basic-AFL is a full hyper-AFL, but not vice versa. The class of OI macro languages (i.e., indexed languages, i.e., nested stack automaton languages) is a full basic-AFL, properly containing the smallest full basic-AFL. The latter is generated by the ultrabasic macro grammars and accepted by the nested stack automata with bounded depth of nesting (and properly contains the stack languages, the ETOL languages, i.e., the smallest full hyper-AFL, and the basic macro languages). The full basic-AFLs are characterized by bounded nested stack controlled machines
Hairdressing in groups: a survey of combings and formal languages
A group is combable if it can be represented by a language of words
satisfying a fellow traveller property; an automatic group has a synchronous
combing which is a regular language. This article surveys results for combable
groups, in particular in the case where the combing is a formal language.Comment: 17 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTMon1/paper24.abs.htm
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