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- de Oliveira Oliveira, Mateus, 1982-
(författare)
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Combinatorial Slice Theory
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Slices are digraphs that can be composed together to form larger digraphs.In this thesis we introduce the foundations of a theory whose aim is to provide ways of defining and manipulating infinite families of combinatorial objects such as graphs, partial orders, logical equations etc. We give special attentionto objects that can be represented as sequences of slices. We have successfully applied our theory to obtain novel results in three fields: concurrency theory,combinatorics and logic. Some notable results are:Concurrency Theory:We prove that inclusion and emptiness of intersection of the causalbehavior of bounded Petri nets are decidable. These problems had been open for almost two decades.We introduce an algorithm to transitively reduce infinite familiesof DAGs. This algorithm allows us to operate with partial order languages defined via distinct formalisms, such as, Mazurkiewicztrace languages and message sequence chart languages.Combinatorics:For each constant z ∈ N, we define the notion of z-topological or-der for digraphs, and use it as a point of connection between the monadic second order logic of graphs and directed width measures, such as directed path-width and cycle-rank. Through this connection we establish the polynomial time solvability of a large numberof natural counting problems on digraphs admitting z-topological orderings.Logic:We introduce an ordered version of equational logic. We show thatthe validity problem for this logic is fixed parameter tractable withrespect to the depth of the proof DAG, and solvable in polynomial time with respect to several notions of width of the equations being proved. In this way we establish the polynomial time provability of equations that can be out of reach of techniques based on completion and heuristic search.
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| 2. |
- Rezine, Othmane, 1982-
(författare)
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Verification of networks of communicating processes : Reachability problems and decidability issues
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Computer systems are used in almost all aspects of our lives and our dependency on them keeps on increasing. When computer systems are used to handle critical tasks, any software failure can cause severe human and/or material losses. Therefore, for such applications, it is important to detect software errors at an early stage of software development. Furthermore, the growing use of concurrent and distributed programs exponentially increases the complexity of computer systems, making the problem of detecting software errors even harder (if not impossible). This calls for defining systematic and efficient techniques to evaluate the safety and the correctness of programs. The aim of Model-Checking is to analyze automatically whether a given program satisfies its specification. Early applications of Model-Checking were restricted to systems whose behaviors can be captured by finite graphs, so called finite-state systems. Since many computer systems cannot be modeled as finite-state machines, there has been a growing interest in extending the applicability of Model-Checking to infinite-state systems.The goal of this thesis is to extend the applicability of Model Checking for three instances of infinite-state systems: Ad-Hoc Networks, Dynamic Register Automata and Multi Pushdown Systems. Each one of these instances models challenging types of networks of communicating processes. In both Ad-Hoc Networks and Dynamic Register Automata, communication is carried through message passing. In each type of network, a graph topology models the communication links between processes in the network. The graph topology is static in the case of Ad-Hoc Networks while it is dynamic in the case of Dynamic Register Automata. The number of processes in both types of networks is unbounded. Finally, we consider Multi Pushdown Systems, a model used to study the behaviors of concurrent programs composed of sequential recursive sequential programs communicating through a shared memory.
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