Related papers: A concise proof of Commoner's theorem
In this paper the correspondence between safe Petri nets and event structures, due to Nielsen, Plotkin and Winskel, is extended to arbitrary nets without self-loops, under the collective token interpretation. To this end we propose a more…
This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions,…
This paper explores the connection between two central results in the proof theory of classical logic: Gentzen's cut-elimination for the sequent calculus and Herbrands "fundamental theorem". Starting from Miller's expansion-tree-proofs, a…
A very short proof of Kneser's theorem via transversal is given.
Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.
In recent work, the second and third authors introduced a technique for reachability checking in 1-bounded Petri nets, based on wiring decompositions, which are expressions in a fragment of the compositional algebra of nets with boundaries.…
This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent,…
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.
This paper contains introductory material on Petri nets and Groebner basis theory and makes some observations on the relation between the two areas. The aim of the paper is to show how Groebner basis procedures can be applied to the problem…
This paper presents a new formal method for verification of quantum communication protocols. By extending the symbolic system of Petri nets, we can define quantum pure states in Petri-net settings. Therefore, it is possible to emerge a…
We define the concept of collaborative theorem proving and outline our plan to make it a reality. We believe that a successful implementation of collaborative theorem proving is a necessary prerequisite for the formal verification of large…
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
A marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. Characterizing the class of systems that are lucent is…
We give a self-contained treatment of the theory of persistence modules indexed over the real line. We give new proofs of the standard results. Persistence diagrams are constructed using measure theory. Linear algebra lemmas are simplified…
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.
Convergence is a fundamental topic in analysis that is most commonly modelled using topology. However, there are many natural convergences that are not given by any topology; e.g., convergence almost everywhere of a sequence of measurable…
In this paper we introduce the notion of spread net. Spread nets are (safe) Petri nets equipped with vector clocks on places and with ticking functions on transitions, and are such that vector clocks are consistent with the ticking of…