## Abstract

Boolean functions are characterized by the unique structure of their solution space. Some properties of the solution space, such as the possible existence of a solution, are well sought after but difficult to obtain. To better reason about such properties, we define transformations as functions that change one Boolean function to another while maintaining some properties of the solution space. We explore transformations of Boolean functions, compactly described as Boolean formulas, where the property is to maintain is the number of solutions in the solution spaces. We first discuss general characteristics of such transformations. Next, we reason about the computational complexity of transforming one Boolean formula to another. Finally, we demonstrate the versatility of transformations by extensively discussing transformations of Boolean formulas to “blocks,” which are solution spaces in which the set of solutions makes a prefix of the solution space under a lexicographic order of the variables.

Original language | English |
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Title of host publication | 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2019 |

Editors | Arkadev Chattopadhyay, Paul Gastin |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959771313 |

DOIs | |

State | Published - Dec 2019 |

Event | 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2019 - Bombay, India Duration: 11 Dec 2019 → 13 Dec 2019 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 150 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2019 |
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Country/Territory | India |

City | Bombay |

Period | 11/12/19 → 13/12/19 |

### Bibliographical note

Funding Information:Funding Jeffrey M. Dudek: Supported by NSF grants DMS-1547433 and IIS-1527668, by the Big-Data Private-Cloud Research Cyberinfrastructure MRI-award funded by NSF under grant CNS-1338099, by the Ken Kennedy Institute Computer Science & Engineering Enhancement Fellowship funded by the Rice Oil & Gas HPC Conference, and by the Ken Kennedy Institute 2017/18 Cray Graduate Fellowship.

Funding Information:

Jeffrey M. Dudek: Supported by NSF grants DMS-1547433 and IIS-1527668, by the Big-Data Private-Cloud Research Cyberinfrastructure MRI-award funded by NSF under grant CNS-1338099, by the Ken Kennedy Institute Computer Science & Engineering Enhancement Fellowship funded by the Rice Oil & Gas HPC Conference, and by the Ken Kennedy Institute 2017/18 Cray Graduate Fellowship.

Publisher Copyright:

© Jeffrey M. Dudek and Dror Fried; licensed under Creative Commons License CC-BY.

## Keywords

- Boolean Formulas
- Boolean Functions
- Model Counting
- Transformations