# Cohesiveness in promise problems

@article{Brandt2013CohesivenessIP, title={Cohesiveness in promise problems}, author={U. Brandt and Hermann K.-G. Walter}, journal={RAIRO Theor. Informatics Appl.}, year={2013}, volume={47}, pages={351-369} }

Promise problems have been introduced in 1985 by S. Even e.a. as a generalization of decision problems. Using a very general approach we study solvability and unsolvability conditions for promise problems of set and language families. We show, that cores of unsolvability are completely determined by partitions of cohesive sets. We prove the existence of cores in unsolvable promise problems assuming certain closure properties for the given set family. Connections to immune sets and complexity…

## 2 Citations

### Unsolvability Cores in Classification Problems

- MathematicsLog. Methods Comput. Sci.
- 2014

The main results are a characterization of unsolvability cores via cohesiveness and existence theorems for such cores in unsolvable classification problems and the existence of conditional cores with recursive components for language families that admit an uniform solution for the word problem.

### Real Benefit of Promises and Advice

- Computer ScienceCiE
- 2013

This work advertises constant-size advice and explores its theoretical impact on the complexity of classification problems – a natural generalization of promise problems – and on real functions and operators.

## References

SHOWING 1-10 OF 12 REFERENCES

### On Promise Problems: A Survey

- MathematicsEssays in Memory of Shimon Even
- 2006

This article surveys some of the applications that this notion of promise problems has found in the twenty years that elapsed, including the notion of “unique solutions”, the formulation of "gap problems" as capturing various approximation tasks, the identification of complete problems, and the enabling of presentations that better distill the essence of various proofs.

### The Complexity of Promise Problems with Applications to Public-Key Cryptography

- Mathematics, Computer ScienceInf. Control.
- 1984

### Real Benefit of Promises and Advice

- Computer ScienceCiE
- 2013

This work advertises constant-size advice and explores its theoretical impact on the complexity of classification problems – a natural generalization of promise problems – and on real functions and operators.

### Recursively enumerable sets and degrees

- Mathematics
- 1987

TABLE OF CONTENTS Introduction Chapter I. The relation of the structure of an r.e. set to its degree. 1. Post's program and simple sets. 2. Dominating functions and quotient lattices. 3. Maximal sets…

### Theory of Recursive Functions and Effective Computability

- Computer Science
- 1969

If searching for the ebook by Hartley Rogers Theory of Recursive Functions and Effective Computability in pdf format, then you've come to the faithful site. We presented the complete version of this…

### Word, language, grammar

- Linguistics
- 1997

This first volume of the Handbook of Formal Languages gives a comprehensive authoritative exposition on the core of language theory in what is perhaps the most informative single volume in the history of theoretical computer science.

### The existence and density of generalized complexity cores

- Physics, MathematicsJACM
- 1987

It is shown that if C is a countable class of sets of strings that is closed under finite union and finite variation, then every infinite set not in C has a proper hard core with respect to C.

### On Promise Problems (a survey in memory of Shimon Even [1935-2004])

- MathematicsElectron. Colloquium Comput. Complex.
- 2005

### An Introduction to Formal Language Theory

- Computer ScienceTexts and Monographs in Computer Science
- 1988

This volume intended to serve as a text for upper undergraduate and graduate level students and special emphasis is given to the role of algebraic techniques in formal language theory through a chapter devoted to the fixed point approach to the analysis of context-free languages.