132 research outputs found
Free-cut elimination in linear logic and an application to a feasible arithmetic
International audienceWe prove a general form of 'free-cut elimination' for first-order theories in linear logic, yielding normal forms of proofs where cuts are anchored to nonlogical steps. To demonstrate the usefulness of this result, we consider a version of arithmetic in linear logic, based on a previous axiomatisation by Bellantoni and Hofmann. We prove a witnessing theorem for a fragment of this arithmetic via the 'witness function method', showing that the provably convergent functions are precisely the polynomial-time functions. The programs extracted are implemented in the framework of 'safe' recursive functions, due to Bellantoni and Cook, where the ! modality of linear logic corresponds to normal inputs of a safe recursive program
Automatic Equivalence Structures of Polynomial Growth
In this paper we study the class EqP of automatic equivalence structures of the form ?=(D, E) where the domain D is a regular language of polynomial growth and E is an equivalence relation on D. Our goal is to investigate the following two foundational problems (in the theory of automatic structures) aimed for the class EqP. The first is to find algebraic characterizations of structures from EqP, and the second is to investigate the isomorphism problem for the class EqP. We provide full solutions to these two problems. First, we produce a characterization of structures from EqP through multivariate polynomials. Second, we present two contrasting results. On the one hand, we prove that the isomorphism problem for structures from the class EqP is undecidable. On the other hand, we prove that the isomorphism problem is decidable for structures from EqP with domains of quadratic growth
Initial Limit Datalog:a new extensible class of decidable constrained Horn clauses
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types) of the first-order language limit Datalog Z (a fragment of Datalog modulo linear integer arithmetic), but can be instantiated with any suitable background theory. For example, the fragment is decidable over any countable well-quasi-order with a decidable first-order theory, such as natural number vectors under componentwise linear arithmetic, and words of a bounded, context-free language ordered by the subword relation. Formulas of initial limit Datalog have the property that, under some assumptions on the background theory, their satisfiability can be witnessed by a new kind of term model which we call entwined structures. Whilst the set of all models is typically uncountable, the set of all entwined structures is recursively enumerable, and model checking is decidable
Realizable and Context-Free Hyperlanguages
Hyperproperties lift conventional trace-based languages from a set of execution traces to a set of sets of executions. From a formal-language perspective, these are sets of sets of words, namely hyperlanguages. Hyperautomata are based on classical automata models that are lifted to handle hyperlanguages. Finite hyperautomata (NFH) have been suggested to express regular hyperproperties. We study the realizability problem for regular hyperlanguages: given a set of languages, can it be precisely described by an NFH? We show that the problem is complex already for singleton hyperlanguages.
We then go beyond regular hyperlanguages, and study context-free hyperlanguages. We show that the natural extension to context-free hypergrammars is highly undecidable. We then suggest a refined model, namely synchronous hypergrammars, which enables describing interesting non-regular hyperproperties, while retaining many decidable properties of context-free grammars
Revisiting Membership Problems in Subclasses of Rational Relations
We revisit the membership problem for subclasses of rational relations over
finite and infinite words: Given a relation R in a class C_2, does R belong to
a smaller class C_1? The subclasses of rational relations that we consider are
formed by the deterministic rational relations, synchronous (also called
automatic or regular) relations, and recognizable relations. For almost all
versions of the membership problem, determining the precise complexity or even
decidability has remained an open problem for almost two decades. In this
paper, we provide improved complexity and new decidability results. (i) Testing
whether a synchronous relation over infinite words is recognizable is
NL-complete (PSPACE-complete) if the relation is given by a deterministic
(nondeterministic) omega-automaton. This fully settles the complexity of this
recognizability problem, matching the complexity of the same problem over
finite words. (ii) Testing whether a deterministic rational binary relation is
recognizable is decidable in polynomial time, which improves a previously known
double exponential time upper bound. For relations of higher arity, we present
a randomized exponential time algorithm. (iii) We provide the first algorithm
to decide whether a deterministic rational relation is synchronous. For binary
relations the algorithm even runs in polynomial time
Decision Problems for Subclasses of Rational Relations over Finite and Infinite Words
We consider decision problems for relations over finite and infinite words
defined by finite automata. We prove that the equivalence problem for binary
deterministic rational relations over infinite words is undecidable in contrast
to the case of finite words, where the problem is decidable. Furthermore, we
show that it is decidable in doubly exponential time for an automatic relation
over infinite words whether it is a recognizable relation. We also revisit this
problem in the context of finite words and improve the complexity of the
decision procedure to single exponential time. The procedure is based on a
polynomial time regularity test for deterministic visibly pushdown automata,
which is a result of independent interest.Comment: v1: 31 pages, submitted to DMTCS, extended version of the paper with
the same title published in the conference proceedings of FCT 2017; v2: 32
pages, minor revision of v1 (DMTCS review process), results unchanged; v3: 32
pages, enabled hyperref for Figure 1; v4: 32 pages, add reference for known
complexity results for the slenderness problem; v5: 32 pages, added DMTCS
metadat
Theories of Informetrics and Scholarly Communication
Scientometrics have become an essential element in the practice and evaluation of science and research, including both the evaluation of individuals and national assessment exercises. Yet, researchers and practitioners in this field have lacked clear theories to guide their work. As early as 1981, then doctoral student Blaise Cronin published "The need for a theory of citing" —a call to arms for the fledgling scientometric community to produce foundational theories upon which the work of the field could be based. More than three decades later, the time has come to reach out the field again and ask how they have responded to this call.
This book compiles the foundational theories that guide informetrics and scholarly communication research. It is a much needed compilation by leading scholars in the field that gathers together the theories that guide our understanding of authorship, citing, and impact
Theories of Informetrics and Scholarly Communication
Scientometrics have become an essential element in the practice and evaluation of science and research, including both the evaluation of individuals and national assessment exercises. Yet, researchers and practitioners in this field have lacked clear theories to guide their work. As early as 1981, then doctoral student Blaise Cronin published The need for a theory of citing - a call to arms for the fledgling scientometric community to produce foundational theories upon which the work of the field could be based. More than three decades later, the time has come to reach out the field again and ask how they have responded to this call. This book compiles the foundational theories that guide informetrics and scholarly communication research. It is a much needed compilation by leading scholars in the field that gathers together the theories that guide our understanding of authorship, citing, and impact
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