A Polynomial Translation of -Calculus (FCP) to Safe Petri Nets Roland Meyer 1 , Victor Khomenko 2 , and Reiner Hüchting 1 1 Department of Computing Science, University of Kaiserslautern, Germany 2 School of Computing Science, Newcastle University, UK
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A Polynomial Translation of - Calculus (FCP) to Safe Petri Nets
A Polynomial Translation of - Calculus (FCP) to Safe Petri Nets. Roland Meyer 1 , Victor Khomenko 2 , and Reiner H ü chting 1 1 Department of Computing Science, University of Kaiserslautern, Germany 2 School of Computing Science, Newcastle University, UK. - Calculus. - PowerPoint PPT Presentation
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A Polynomial Translation of -Calculus (FCP) to Safe Petri Nets
Roland Meyer1, Victor Khomenko2, and Reiner Hüchting1
1Department of Computing Science,University of Kaiserslautern, Germany
2School of Computing Science,Newcastle University, UK
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-Calculus
• A formalism (process algebra) for modelling mobile and reconfigurable systems
• Processes communicate by message passing: channels are sent via channels passing an IP address or hyperlink passing a pointer/reference to a procedure
• New fresh channels can be dynamically created• (Logical) interconnect topology changes over time
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-Calculus: example
P1 P2 P3…
Scheduler
Task generators
TG1 TG2 TGk…
Array of processors
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-Calculus Syntax
P ::= 0| K a⌊ 1,…,an⌋| P + P| P | P| .P| a:P ::= a<b>| a(x)|
No replication operator ‘!’ – using recursive definitions of the form K a⌊ 1,…,an :=P⌋ instead
Input prefix a(x).P and restriction x:P bind name x in PNOCLASH assumption (can always be enforced by -
conversion): • each name is bound at most once• the sets of bound and free names are disjoint
stop call choice Parallel composition
prefix restriction
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Finite Control Processes
• -Calculus is expressive (Turing-powerful), so nothing is decidable
• Wanted: a (syntactic) fragment that is decidable but retains a reasonable degree of expressiveness sufficient for modelling practical mobile and reconfigurable systems
• Finite Control Processes (FCP): parallel composition of a fixed number of sequential (i.e. not using the | operator) processes (threads)
• Good compromise between expressiveness and verifiability
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Motivation for FCPPN translation
• FCPs have complicated semantics, and thus difficult for model checking: checking if two terms are structurally congruent
is graph isomorphism complete difficult to use condensed representations of the
state space difficult to use reductions when exploring the
state space• In contrast, safe low-level PNs are well suited for
model checking, with many efficient heuristics available
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Our contribution
Safe low-level PNs:Efficient verification
Not convenient for reconfigurability
FCPs:Convenient for
modelling reconfigurability
Verification is hardGap
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Complexity-theoretic considerations• Any reachable state of an FCP can be represented by a
term bounded by the FCP’s size• Hence an FCP can be simulated by a Turing machine
with linear in the FCP’s size tape (characterises PSPACE)
• A Turing machine with a bounded tape can be simulated by a safe low-level PN of polynomial size
• Hence a polynomial translation from FCPs to safe low-level PNs must exist
• This argument is constructive, but the resulting PN would be big and ugly
• Wanted: A natural polynomial FCPPN translation, suitable for practical verification
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Related work• Much work concerning -CalculusPN translations
has been performed• Mostly theoretical, often concerning the full -
Calculus and so results in infinite PNs or undecidable PN classes (inhibitor arcs, coloured with infinite sets of colours, etc.)
• Existing FCPPN translations (or restrictions of -CalculusPN translations to FCPs) are non-polynomial and/or have an unnecessarily powerful target formalism (coloured / inhibitor / transfer PNs)