Petri Nets for Business Process Modeling

<p>A system of equations with five equations and six variables.</p> Signup and view all the answers

<p>The transitions i1, i3, and i5 fire the same number of times.</p> Signup and view all the answers

<p>Petri nets are used for modeling concurrent systems, while finite automata are used for modeling sequential systems.</p> Signup and view all the answers

<p>Places, transitions, and arcs.</p> Signup and view all the answers

<p>Reachability graph and invariants.</p> Signup and view all the answers

<p>A property that does not change through the execution of the token game.</p> Signup and view all the answers

<p>Two types.</p> Signup and view all the answers

<p>To define the semantics of languages</p> Signup and view all the answers

<p>Computations are executed independently of one another</p> Signup and view all the answers

<p>A pair of nodes and a set of edges</p> Signup and view all the answers

<p>A graph with two different types of nodes</p> Signup and view all the answers

<p>Finite automata</p> Signup and view all the answers

<p>Petri nets are used for concurrent computations, while finite automata are used for sequential computations</p> Signup and view all the answers

<p>A special type of graph</p> Signup and view all the answers

<p>They can model concurrent processes</p> Signup and view all the answers

<p>A bipartite graph with two disjoint sets of nodes, called places and transitions, and arcs between them</p> Signup and view all the answers

<p>To model the dynamic behavior of systems</p> Signup and view all the answers

<p>The set of all input places of the transition</p> Signup and view all the answers

<p>When all input places of the transition contain at least one token</p> Signup and view all the answers

<p>One token is removed from each input place and one token is added to each output place</p> Signup and view all the answers

<p>A function that assigns a number of tokens to every place</p> Signup and view all the answers

<p>The set of all nodes to which there is an edge from the node</p> Signup and view all the answers

<p>Petri nets model dynamic behavior, while finite automata do not</p> Signup and view all the answers

<p>To assign an initial number of tokens to each place</p> Signup and view all the answers

<p>A set of rules for describing the movement of tokens through the network</p> Signup and view all the answers

<p>The transition t is enabled in state s.</p> Signup and view all the answers

<p>To model the flow of tokens through the net.</p> Signup and view all the answers

<p>A transition that generates tokens in two places.</p> Signup and view all the answers

<p>A Petri net where every place has at most one token.</p> Signup and view all the answers

<p>A Petri net with exactly one start and one final place.</p> Signup and view all the answers

<p>To assign weights to the edges of the net.</p> Signup and view all the answers

<p>The Petri net is in state s' after the sequence T of transitions has fired.</p> Signup and view all the answers

<p>That all resources required for the transition are available.</p> Signup and view all the answers

<p>To model the branching of processes.</p> Signup and view all the answers

<p>That each split has a corresponding join.</p> Signup and view all the answers

<p>It is suitable for modeling processes that run multiple times in parallel</p> Signup and view all the answers

<p>The number of tokens consumed and generated corresponds to the weights of the input and output edges</p> Signup and view all the answers

<p>A situation where different components block each other, preventing further actions</p> Signup and view all the answers

<p>A property that ensures every transition can be activated</p> Signup and view all the answers

<p>A property that ensures a place does not contain more than k tokens</p> Signup and view all the answers

<p>A Petri net that never contains a deadlock</p> Signup and view all the answers

<p>A property that ensures a system always terminates</p> Signup and view all the answers

<p>The properties of liveness, safety, and deadlock-freeness</p> Signup and view all the answers

<p>It is not live, safe, and contains a deadlock</p> Signup and view all the answers

<p>It is live, but not safe and does not contain a deadlock</p> Signup and view all the answers

<p>To ensure that every philosopher can eat after a certain time and that two neighboring philosophers do not permanently block each other</p> Signup and view all the answers

<p>To ensure that only one component can go into a critical state at a time</p> Signup and view all the answers

<p>Is it possible to guarantee from every reachable state that a certain transition can be executed again at some point?</p> Signup and view all the answers

<p>To analyze whether certain desired or undesired states can be reached</p> Signup and view all the answers

<p>The configuration and distribution of tokens</p> Signup and view all the answers

<p>To identify properties that remain unchanged by sequences of transitions</p> Signup and view all the answers

<p>The interaction of different concurrent systems</p> Signup and view all the answers

<p>Is the number of tokens (in total or at certain places) bounded?</p> Signup and view all the answers

<p>To define the set of possible markings of a Petri net</p> Signup and view all the answers

<p>Is it guaranteed that for every possible sequence of transitions a deadlock will be reached?</p> Signup and view all the answers

<p>The former is undecidable, while the latter is decidable.</p> Signup and view all the answers

<p>To represent the marking in a compact and understandable way.</p> Signup and view all the answers

<p>It represents the token consumption of the transition as well as the generation of tokens at the places.</p> Signup and view all the answers

<p>The i-th column of the matrix N.</p> Signup and view all the answers

<p>A certain combination of the number of tokens does not change.</p> Signup and view all the answers

<p>Place invariants are linear combinations of place tokens, while transition invariants are linear combinations of transition tokens.</p> Signup and view all the answers

<p>To describe the behavior of the Petri net.</p> Signup and view all the answers

<p>M = (n1, ..., nq) where ni is the number of tokens at place pi.</p> Signup and view all the answers

<p>M1 + t = M2.</p> Signup and view all the answers

<p>Business process modeling.</p> Signup and view all the answers

<p>To derive important properties of the modeled system</p> Signup and view all the answers

<p>The number of tokens remains unchanged if it contains the same number of transitions</p> Signup and view all the answers

<p>A system of equations with five equations and six variables</p> Signup and view all the answers

<p>To add the possibility of describing and analyzing the behavior of concurrent systems</p> Signup and view all the answers

<p>Places, transitions, and arcs</p> Signup and view all the answers

<p>One is used to analyze the behavior of systems and the other is used to identify properties that do not change through the execution of the token game</p> Signup and view all the answers

<p>It represents the two loops in the Petri net</p> Signup and view all the answers

<p>They can be used to describe and analyze the behavior of concurrent systems</p> Signup and view all the answers

<p>It remains constant during the execution of transitions</p> Signup and view all the answers

<p>x1 · n1 + … + xq · nq = c</p> Signup and view all the answers

<p>x1 = x3 = 0 and x2 = x4 = x5</p> Signup and view all the answers

<p>The transpose of the incidence matrix N</p> Signup and view all the answers

<p>A sequence of transitions that does not change the marking of the Petri net</p> Signup and view all the answers

<p>A vector that describes the number of times each transition appears in the sequence</p> Signup and view all the answers

<p>The change in the number of tokens at each place must be zero</p> Signup and view all the answers

<p>To describe properties of the Petri net that remain constant during the execution of transitions</p> Signup and view all the answers

<p>They provide a way to describe properties of the Petri net that remain constant during the execution of transitions</p> Signup and view all the answers

<p>Place Invariants describe properties of the Petri net that remain constant during the execution of transitions, while Transition Invariants describe the behavior of the Petri net during the execution of transitions</p> Signup and view all the answers

<p>The set of all states s′ that can be reached from s</p> Signup and view all the answers

<p>To prove that two trains can never enter the single-track line from different directions</p> Signup and view all the answers

<p>It is not k-bounded, and the reachability graph becomes infinite</p> Signup and view all the answers

<p>It can become very large and confusing relatively quickly</p> Signup and view all the answers

<p>The problem of whether an algorithm exists to decide the reachability of a marking</p> Signup and view all the answers

<p>It is in EXPSPACE</p> Signup and view all the answers

<p>A property of a Petri net that does not change under certain transformations</p> Signup and view all the answers

<p>They can be used to prove properties like mutual exclusion</p> Signup and view all the answers

<p>The reachability graph is used to prove properties like mutual exclusion, while invariants are used to prove properties like liveness</p> Signup and view all the answers

<p>The equivalence problem</p> Signup and view all the answers