R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, TU-M unchen, 1997.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and study infinitestate models that can verify interesting properties such as reachability, safety, liveness, etc. The infinite state models that have been investigated includes timed automata [3] pushdown automata [7, 18] various versions of counter machines [11, 17] and process calculi [28, 9]. A timed automaton is basically a finite state automaton with finitely many unbounded clocks that can be tested and reset. Since their introduction and the development of appropriate model checking algorithms [2, 5, 21] timed automata have become a standard model for investigating verification ....

R. Mayr. Decidability and complexity of model-checking problems for infinite state systems, Ph.D. Thesis, Inst. fur Informatik, Techn. Universitat Munchen, 1998

....System (LTS) The design and verification of an LTS given a functional specification, is not straightforward. One of the main problems that has to be contended with, is the state explosion problem. Indeed, many systems can only be described by infinite states which calls for new design approaches [5]. Some of the approaches that have been proposed in the literature include abstraction, categorization, bisimulation, etc. However, another common problem that has not received adequate attention is the design and verification of a reactive system in the face of concurrent interactive processes. ....

Richard Mayr. Decidability and Complexity of Model-Checking Problems for Infinite State Systems. PhD Thesis, Technical University of Munich, Munich, Germany, 1997.

....rules) in order to compute the exact effect of their iteration. In [BJNT00,Tou00] widening techniques on automata and transducers are defined for regular model checking. 14 The use of rewriting systems as models for infinite state systems has been considered for instance in [Cau92,Mol96,May98] These works address different questions from the one considered here. They are concerned with the decidability and the complexity of behavioral equivalences such as bisimulation [Cau92,Mol96] or model checking against various propositional temporal logics [May98] Rewriting systems are also ....

....for instance in [Cau92,Mol96,May98] These works address different questions from the one considered here. They are concerned with the decidability and the complexity of behavioral equivalences such as bisimulation [Cau92,Mol96] or model checking against various propositional temporal logics [May98] Rewriting systems are also used to model parametrized networks of identical processes in [FO97] where rewriting techniques are applied for invariant checking, but no algorithms for automatic computation of the closure of languages by rewriting systems are provided. Finally, we have considered ....

R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite State Systems. PhD Thesis, Technische Universitaet Muenchen, April 1998.

....mainly due to the possibility of these models to describe grid like structures, an easy cause of undecidability. The only positive result for this class of infinite state models concerns the logic EF and the process class BPP [52] which turn out to impose a PSPACE complete model checking problem [109, 111]. 3.2.1 BPA Hennessy Milner Logic Since BPA processes are finite branching, model checking HML is trivially decidable. As for all finite branching processes, the given BPA process has only to be unfolded up to depth jOEj, for a HML formula OE at hand, as validity of OE can then readily be ....

....the other hand, Esparza also proved a lower bound for the problem by a reduction of the validity problem for quantified boolean formula (QBF) which is known to be PSPACE complete. This PSPACE hardness result, which even holds for BPPs that describe finite state systems, was complemented by Mayr [109, 111] who showed that the model checking problem for full BPP only requires polynomial space, thereby establishing that it is PSPACE complete. Thus adding recursion to finite state BPPs does not increase the complexity of model checking. A further consequence of Mayr s result is that for a fixed ....

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R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, Technische Universitat Munchen, 1998.

....variables are global. For this it will suffice to apply a beautiful extension of Theorem 1 recently proved by Lugiez and Schnoebelen in [18] In order to model parallel flow graph systems by process systems we need to extend these to parallel process systems (also called process rewrite systems in [20]) An agent of a parallel process system is a tree whose root and internal nodes are labelled with either Delta or k, representing sequential and parallel composition, and whose leaves are labelled with agent variables. So, for instance, the intended meaning of the tree (XkY ) Delta Z is that X ....

R. Mayr. Decidability and Complexity of Model Checking Problems for InfiniteState Systems. Ph.D. thesis, Technische Universitat Munchen, 1998.

....PA and pushdown processes. We prove that a large class of bisimulation like equivalences (including e.g. strong and weak bisimilarity) is decidable between PAD and finite state processes, utilizing previously established results on decidability of the model checking problem for EF logic [May97a, May98] We also provide several undecidability results to complete the picture we show that any reasonable bisimulation like equivalence is undecidable between state extended PA processes and finite state ones. Moreover, even in case of state extended BPP processes (which form a natural subclass of ....

....The decidability of model checking with the logic EFR depends on the constraints that correspond to R. It has been shown in [May97a] that model checking PAprocesses with the logic EF is decidable for the class of decomposable constraints. This result has been generalized to PAD processes in [May98] These constraints are called decomposable, because they can be decomposed w.r.t. sequential and parallel composition. The formal definition is as follows: A set of decomposable constraints DC is a finite set of unary predicates on finite sequences of actions that contains the predicates true ....

R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, TU-Munchen, 1998.

....the modal calculus to construct characteristic formulae [33] We show that the much simpler logic EF (a fragment of CTL and the modal calculus) suOEces. This is signicant, because model checking with EF is decidable for many more classes of innite state systems than with the modal calculus [10,20,24]. Then we apply the designed method to the class of PAD processes (dened in [21] which properly subsumes all PA and pushdown processes. We prove that a large class of bisimulation like equivalences (including, e.g. strong and weak bisimilarity) is decidable between PAD and nite state processes, ....

....all PA and pushdown processes. We prove that a large class of bisimulation like equivalences (including, e.g. strong and weak bisimilarity) is decidable between PAD and nite state processes, utilizing previously established results on decidability of the model checking problem for the logic EF [23,20,24,19]. We also provide several undecidability results to complete the picturewe show that any reasonable bisimulation like equivalence is undecidable between state extended PA processes and nite state ones. Moreover, even in the case of state extended BPP processes (which form a natural subclass of ....

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R. Mayr. Decidability and Complexity of Model Checking Problems for InniteState Systems. PhD thesis, TU-M#nchen, 1998.

....Thus, it was conjectured that a polynomial algorithm should also exist for general (unnormed) BPP. This belief was reinforced by the fact that many other problems for BPP are polynomial: boundedness [17] termination, liveness, partial) deadlock reachability and (partial) livelock reachability [21, 22]. On the other hand there are also hard problems for BPP: reachability is NP complete [8] some model checking problems are PSPACE complete [20, 22] or even undecidable [9] Our contribution. We show that strong bisimilarity for BPP is co NP hard (thus proving the above mentioned conjecture ....

.... other problems for BPP are polynomial: boundedness [17] termination, liveness, partial) deadlock reachability and (partial) livelock reachability [21, 22] On the other hand there are also hard problems for BPP: reachability is NP complete [8] some model checking problems are PSPACE complete [20, 22] or even undecidable [9] Our contribution. We show that strong bisimilarity for BPP is co NP hard (thus proving the above mentioned conjecture wrong) We also show that weak bisimilarity for BPP is Pi p 2 hard, thus improving a previously established NP lower bound [31] Finally, we show ....

R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, TU-Munchen, 1998.

....the modal calculus to construct characteristic formulae [33] We show that the much simpler logic EF (a fragment of CTL and the modal calculus) suffices. This is significant, because model checking with EF is decidable for many more classes of infinite state systems than with the modal calculus [10,20,24]. Then we apply the designed method to the class of PAD processes (defined in [21] which properly subsumes all PA and pushdown processes. We prove that a large class of bisimulation like equivalences (including, e.g. strong and weak bisimilarity) is decidable between PAD and finite state ....

....all PA and pushdown processes. We prove that a large class of bisimulation like equivalences (including, e.g. strong and weak bisimilarity) is decidable between PAD and finite state processes, utilizing previously established results on decidability of the model checking problem for the logic EF [23,20,24,19]. We also provide several undecidability results to complete the picture we show that any reasonable bisimulation like equivalence is undecidable between state extended PA processes and finite state ones. Moreover, even in the case of state extended BPP processes (which form a natural subclass ....

[Article contains additional citation context not shown here]

R. Mayr. Decidability and Complexity of Model Checking Problems for InfiniteState Systems. PhD thesis, TU-Munchen, 1998.

....It is a common generalization of Petri nets and PA processes and it is strictly more general than both of them (e.g. PAN can describe all Chomsky 2 languages while Petri nets cannot) 8) S; G) PRS are a common generalization of pushdown processes and PAprocesses. They are called PAD (PA PD) in [23]. 9) The most general case is (G; G) PRS (here simply called PRS) PRS have been introduced in [18,22] They subsume all the previously mentioned classes. What does it mean that parallel sequential arbitrary composition is allowed in terms on the left right hand sides of rules The general ....

....since EF is a fragment of the alternation free modal calculus [11,7] Model checking Petri nets with EF has been shown to be undecidable [11,7] by reduction of the reachability set containment problem for Petri nets. Model checking with EF is PSPACE complete for Basic Parallel Processes (BPP) [23,19], and context free processes (BPA) 2,24] For pushdown processes the complexity of model checking with EF is between PSPACEand EXPTIME [2,29,30] It was claimed in [2] that model checking pushdown processes with EF is PSPACE complete. Unfortunately, the given proof is wrong. It assumes that an ....

[Article contains additional citation context not shown here]

R. Mayr. Decidability and Complexity of Model Checking Problems for InfiniteState Systems. PhD thesis, TU-Munchen, 1998.

....all PA and pushdown processes. We prove that a large class of bisimulation like equivalences (including e.g. strong and weak bisimilarity) is decidable between PAD and finite state processes, utilizing previously established results on decidability of the model checking problem for EF logic [15,17]. We also provide several undecidability results to complete the picture we show that any reasonable bisimulation like equivalence is undecidable between state extended PA processes and finite state ones. Moreover, even for stateextended BPP processes (which are a natural subclass of Petri ....

....by true. The decidability of model checking with the logic EFR depends on the constraints that correspond to R. It has been shown in [15] that model checking PA processes with the logic EF is decidable for the class of decomposable constraints. This result has been generalized to PAD processes in [17]. These constraints are called decomposable, because they can be decomposed w.r.t. sequential and parallel composition. The formal definition is as follows: A set of decomposable constraints DC is a finite set of unary predicates on finite sequences of actions that contains the predicates true ....

R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, TU-M unchen, 1998.

....generalization of Petri nets and PA processes and it is strictly more general than both of them (e.g. PAN can describe all Chomsky 2 languages while Petri nets cannot) 8. S; G) PRS are the smallest common generalization of pushdown processes and PA processes. They are called PAD (PA PD) in [May98]. 9. The most general case is (G; G) PRS (here simply called PRS) PRS have been introduced in [May97c] They subsume all the previously mentioned classes. 3 The Intuition In this section we explain the general intuition for the definition of (ff; fi) PRS, i.e. what does it mean that ....

R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, TU-Munchen, 1998.

....For both BPA and pushdown processes, model checking with CTL is only known to be between PSPACE and EXPTIME . To complete the picture, model checking pushdown processes with LTL and the linear time calculus is EXPTIME complete, but polynomial for every fixed formula [BEM97] It has been shown in [May98] that EXPTIME hardness even holds for BPA and LTL. ....

R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, TU-Munchen, 1998.

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R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, TU-M unchen, 1997.

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R. Mayr. Decidability and Complexity of Model Checking Problems for In niteState Systems. PhD thesis, TU-Munchen, 1997.

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R. Mayr. Decidability and Complexity of Model Checking Problems for InfiniteState Systems. Ph.D. thesis, Technische Universitat Munchen, 1998.

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R. Mayr. Decidability and Complexity of Model Checking Problems for InfiniteState Systems. Ph.D. thesis, Technische Universitat Munchen, 1998.

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R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite-State Systems. PhD thesis, TU-Munchen, 1998.

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R. Mayr. Decidability and Complexity of Model Checking Problems for Infinite-State Systems. Phd. thesis, TUM, 1998.

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