Liveness in broadcast networks
We study liveness and model checking problems for broadcast networks, a system model of identical clients communicating via message passing. The first problem that we consider is Liveness Verification . It asks whether there is a computation such that one clients visits a final state infinitely ofte...
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| Vydáno v: | Computing Ročník 104; číslo 10; s. 2203 - 2223 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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01.10.2022
Springer Nature B.V |
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| ISSN: | 0010-485X, 1436-5057 |
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| Abstract | We study liveness and model checking problems for broadcast networks, a system model of identical clients communicating via message passing. The first problem that we consider is
Liveness Verification
. It asks whether there is a computation such that one clients visits a final state infinitely often. The complexity of the problem has been open. It was shown to be
P
-hard but in
EXPSPACE
. We close the gap by a polynomial-time algorithm. The latter relies on a characterization of live computations in terms of paths in a suitable graph, combined with a fixed-point iteration to efficiently check the existence of such paths. The second problem is
Fair Liveness Verification
. It asks for a computation where all participating clients visit a final state infinitely often. We adjust the algorithm to also solve fair liveness in polynomial time. Both problems can be instrumented to answer model checking questions for broadcast networks against linear time temporal logic specifications. The first problem in this context is
Fair Model Checking
. It demands that for all computations of a broadcast network, all participating clients satisfy the specification. We solve the problem via the Vardi–Wolper construction and a reduction to
Liveness Verification
. The second problem is
Sparse Model Checking
. It asks whether each computation has a participating client that satisfies the specification. We reduce the problem to
Fair Liveness Verification
. |
|---|---|
| AbstractList | We study liveness and model checking problems for broadcast networks, a system model of identical clients communicating via message passing. The first problem that we consider is
Liveness Verification
. It asks whether there is a computation such that one clients visits a final state infinitely often. The complexity of the problem has been open. It was shown to be
$$\texttt {P}$$
P
-hard but in
$$\texttt {EXPSPACE}$$
EXPSPACE
. We close the gap by a polynomial-time algorithm. The latter relies on a characterization of live computations in terms of paths in a suitable graph, combined with a fixed-point iteration to efficiently check the existence of such paths. The second problem is
Fair Liveness Verification
. It asks for a computation where all participating clients visit a final state infinitely often. We adjust the algorithm to also solve fair liveness in polynomial time. Both problems can be instrumented to answer model checking questions for broadcast networks against linear time temporal logic specifications. The first problem in this context is
Fair Model Checking
. It demands that for all computations of a broadcast network, all participating clients satisfy the specification. We solve the problem via the Vardi–Wolper construction and a reduction to
Liveness Verification
. The second problem is
Sparse Model Checking
. It asks whether each computation has a participating client that satisfies the specification. We reduce the problem to
Fair Liveness Verification
. We study liveness and model checking problems for broadcast networks, a system model of identical clients communicating via message passing. The first problem that we consider is Liveness Verification . It asks whether there is a computation such that one clients visits a final state infinitely often. The complexity of the problem has been open. It was shown to be P -hard but in EXPSPACE . We close the gap by a polynomial-time algorithm. The latter relies on a characterization of live computations in terms of paths in a suitable graph, combined with a fixed-point iteration to efficiently check the existence of such paths. The second problem is Fair Liveness Verification . It asks for a computation where all participating clients visit a final state infinitely often. We adjust the algorithm to also solve fair liveness in polynomial time. Both problems can be instrumented to answer model checking questions for broadcast networks against linear time temporal logic specifications. The first problem in this context is Fair Model Checking . It demands that for all computations of a broadcast network, all participating clients satisfy the specification. We solve the problem via the Vardi–Wolper construction and a reduction to Liveness Verification . The second problem is Sparse Model Checking . It asks whether each computation has a participating client that satisfies the specification. We reduce the problem to Fair Liveness Verification . We study liveness and model checking problems for broadcast networks, a system model of identical clients communicating via message passing. The first problem that we consider is Liveness Verification. It asks whether there is a computation such that one clients visits a final state infinitely often. The complexity of the problem has been open. It was shown to be P-hard but in EXPSPACE. We close the gap by a polynomial-time algorithm. The latter relies on a characterization of live computations in terms of paths in a suitable graph, combined with a fixed-point iteration to efficiently check the existence of such paths. The second problem is Fair Liveness Verification. It asks for a computation where all participating clients visit a final state infinitely often. We adjust the algorithm to also solve fair liveness in polynomial time. Both problems can be instrumented to answer model checking questions for broadcast networks against linear time temporal logic specifications. The first problem in this context is Fair Model Checking. It demands that for all computations of a broadcast network, all participating clients satisfy the specification. We solve the problem via the Vardi–Wolper construction and a reduction to Liveness Verification. The second problem is Sparse Model Checking. It asks whether each computation has a participating client that satisfies the specification. We reduce the problem to Fair Liveness Verification. |
| Author | Chini, Peter Meyer, Roland Saivasan, Prakash |
| Author_xml | – sequence: 1 givenname: Peter surname: Chini fullname: Chini, Peter email: p.chini@tu-bs.de organization: TU Braunschweig – sequence: 2 givenname: Roland surname: Meyer fullname: Meyer, Roland organization: TU Braunschweig – sequence: 3 givenname: Prakash surname: Saivasan fullname: Saivasan, Prakash organization: The Institute of Mathematical Sciences |
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| SubjectTerms | Algorithms Artificial Intelligence Clients Communication Computation Computer Appl. in Administrative Data Processing Computer Communication Networks Computer Science Information Systems Applications (incl.Internet) Iterative methods Linear programming Message passing Networks Polynomials Software Engineering Special Issue Article Specifications Temporal logic Verification |
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