Search results for "TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES"
showing 10 items of 174 documents
Context-free Languages
1988
In this chapter we shall define a class of rewriting systems called context-free grammars. The left-hand side of a rule in a context-free grammar consists of a single symbol, so that symbols are rewritten “context-freely”. Context-free grammars are of central importance to us because they define the class of context-free languages, the parsing of which is the subject of this book. In this chapter we shall consider some structural properties of context-free grammars which are of importance in parsing. Also, a basic method for recognizing context-free languages will be given.
A lower bound for the Bloch radius of 𝐾-quasiregular mappings
2004
We give a quantitative proof to Eremenko’s theorem (2000), which extends Bloch’s classical theorem to the class of n n -dimensional K K -quasiregular mappings.
Co-learnability and FIN-identifiability of enumerable classes of total recursive functions
1994
Co-learnability is an inference process where instead of producing the final result, the strategy produces all the natural numbers but one, and the omitted number is an encoding of the correct result. It has been proved in [1] that co-learnability of Goedel numbers is equivalent to EX-identifiability. We consider co-learnability of indices in recursively enumerable (r.e.) numberings. The power of co-learnability depends on the numberings used. Every r.e. class of total recursive functions is co-learnable in some r.e. numbering. FIN-identifiable classes are co-learnable in all r.e. numberings, and classes containing a function being accumulation point are not co-learnable in some r.e. number…
On the Finite Satisfiability Problem for the Guarded Fragment with Transitivity
2005
We study the finite satisfiability problem for the guarded fragment with transitivity. We prove that in case of one transitive predicate the problem is decidable and its complexity is the same as the general satisfiability problem, i.e. 2Exptime-complete. We also show that finite models for sentences of GF with more transitive predicate letters used only in guards have essentially different properties than infinite ones.
Learning with belief levels
2008
AbstractWe study learning of predicate logics formulas from “elementary facts,” i.e. from the values of the predicates in the given model. Several models of learning are considered, but most of our attention is paid to learning with belief levels. We propose an axiom system which describes what we consider to be a human scientist's natural behavior when trying to explore these elementary facts. It is proved that no such system can be complete. However we believe that our axiom system is “practically” complete. Theorems presented in the paper in some sense confirm our hypothesis.
Descriptive Complexity, Lower Bounds and Linear Time
1999
This paper surveys two related lines of research: Logical characterizations of (non-deterministic) linear time complexity classes, and non-expressibility results concerning sublogics of existential second-order logic. Starting from Fagin’s fundamental work there has been steady progress in both fields with the effect that the weakest logics that are used in characterizations of linear time complexity classes are closely related to the strongest logics for which inexpressibility proofs for concrete problems have been obtained. The paper sketches these developments and highlights their connections as well as the obstacles that prevent us from closing the remaining gap between both kinds of lo…
Equivalence closure in the two-variable guarded fragment
2015
We consider the satisfiability and finite satisfiability problems for the extension of the two-variable guarded fragment in which an equivalence closure operator can be applied to two distinguished binary predicates. We show that the satisfiability and finite satisfiability problems for this logic are 2-ExpTime-complete. This contrasts with an earlier result that the corresponding problems for the full two-variable logic with equivalence closures of two binary predicates are 2-NExpTime-complete.
Automatic Calibration of an Industrial RGB-D Camera Network Using Retroreflective Fiducial Markers
2019
This paper describes a non-invasive, automatic, and robust method for calibrating a scalable RGB-D sensor network based on retroreflective ArUco markers and the iterative closest point (ICP) scheme. We demonstrate the system by calibrating a sensor network comprised of six sensor nodes positioned in a relatively large industrial robot cell with an approximate size of 10 m × 10 m × 4 m . Here, the automatic calibration achieved an average Euclidean error of 3 c m at distances up to 9.45 m . To achieve robustness, we apply several innovative techniques: Firstly, we mitigate the ambiguity problem that occurs when detecting a marker at long range or low resolution by comparing the…
Transformations that preserve learnability
1996
We consider transformations (performed by general recursive operators) mapping recursive functions into recursive functions. These transformations can be considered as mapping sets of recursive functions into sets of recursive functions. A transformation is said to be preserving the identification type I, if the transformation always maps I-identifiable sets into I-identifiable sets.
Grammars++ for modelling information in text
1999
Abstract Grammars provide a convenient means to describe the set of valid instances in a text database. Flexibility in choosing a grammar can be exploited to provide information modelling capability by designing productions in the grammar to represent entities and relationships of interest to database applications. Additional constraints can be specified by attaching predicates to selected nonterminals in the grammar. When used for database definition, grammars can provide the functionality that users have come to expect of database schemas. Extended grammars can also be used to specify database manipulation, including query, update, view definition, and index specification.