Abstract
This dissertation studies the theory of distributed computing. In the distributed setting, computation is carried out by multiple independent computational units. They communicate with neighbouring units and collectively solve a problem. Systems of this kind are widespread in the information society as well as in the natural world: prime examples include the Internet, multiprocessor computer systems, the cells of a biological organism and human social networks. Therefore it is important to gain knowledge on the fundamental capabilities and limitations of distributed systems.
Our work takes place in the context of deterministic and synchronous messagepassing models of distributed computing. Such models abstract away some possible features of distributed systems, such as asynchrony, congestion and faults, while putting emphasis on the amount of communication needed between the units. The computational units are expected to solve a problem related to the structure of the underlying communication network. More specifically, we study the standard LOCAL model, the standard portnumbering model and several weaker variants of the latter.
The contributions of this dissertation are twofold. First, we give new methods for studying distributed computing by establishing a strong connection between several weak variants of the portnumbering model and corresponding variants of modal logic. This makes it possible to apply existing logical tools, such as bisimulation, to understand computation in the distributed setting. We also give a full characterisation of the relationships between the models of computing, which has implications on the side of mathematical logic.
Second, we prove the existence of various new nonempty complexity classes. One of our results studies the relationship between time and space complexity, which is a relatively new topic in distributed computing research. We demonstrate the existence of a problem that can be solved in a constant amount of space in a very weak model but nonetheless requires a nonconstant amount of time even in a much stronger model of computing. Another result continues the recent success on developing complexity theory for the LOCAL model. We introduce a new technique which shows the existence of an infinite hierarchy of problems with novel time complexities.
Translated title of the contribution  Logiikka ja vaativuus hajautetussa laskennassa 

Original language  English 
Qualification  Doctor's degree 
Awarding Institution 

Supervisors/Advisors 

Publisher  
Print ISBNs  9789526084770 
Electronic ISBNs  9789526084787 
Publication status  Published  2019 
MoE publication type  G5 Doctoral dissertation (article) 
Keywords
 distributed computing
 computational complexity theory
 portnumbering model
 LOCAL model
 graph problems
 LCL problems
 modal logic
 bisimulation
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Lempiäinen, T. (2019). Logic and Complexity in Distributed Computing. Aalto University. http://urn.fi/URN:ISBN:9789526084787