Pushdown Processes: Games and Model Checking

Walukiewicz, Igor

doi:10.7146/brics.v3i54.20057

Cited by 149 publications

(252 citation statements)

References 10 publications

(11 reference statements)

Supporting

Mentioning

245

Contrasting

Order By: Relevance

“…The number of different modal accessibility relations is p + 1 where p is the size of the alphabet in the pushdown games. A close inspection of the ExpTime lower bound proof for this problem [29] shows that p = 1 is sufficient.…”

Section: Proposition 415 ([18 28])mentioning

confidence: 99%

The Complexity of Model Checking Higher-Order Fixpoint Logic

Axelsson¹,

Lange²,

Somla³

2007

Logical Methods in Computer Science

View full text Add to dashboard Cite

Abstract. Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed λ-calculus and the modal µ-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of programs that are not expressible in the modal µ-calculus.This paper provides complexity results for its model checking problem. In particular, we consider those fragments of HFL that are built by using only types of bounded order k and arity m. We establish k-fold exponential time completeness for model checking each such fragment. For the upper bound we use fixpoint elimination to obtain reachability games that are singly-exponential in the size of the formula and k-fold exponential in the size of the underlying transition system. These games can be solved in deterministic linear time. As a simple consequence, we obtain an exponential time upper bound on the expression complexity of each such fragment.The lower bound is established by a reduction from the word problem for alternating (k − 1)-fold exponential space bounded Turing Machines. Since there are fixed machines of that type whose word problems are already hard with respect to k-fold exponential time, we obtain, as a corollary, k-fold exponential time completeness for the data complexity of our fragments of HFL, provided m exceeds 3. This also yields a hierarchy result in expressive power.

show abstract

Section: Proposition 415 ([18 28])mentioning

confidence: 99%

The Complexity of Model Checking Higher-Order Fixpoint Logic

Axelsson¹,

Lange²,

Somla³

2007

Logical Methods in Computer Science

View full text Add to dashboard Cite

show abstract

“…Actually, most of these results are immediate consequences of stronger results about decidable modal mu-calculus, or even the whole monadic second order logic in such systems, see e.g. [Wal01]. It is therefore important to search for larger classes of effectively generated infinite state systems [without necessarily decidable MSO], but in which natural first-order extensions of CTL have decidable model-checking.…”

Section: Introductionmentioning

confidence: 99%

Towards a Model-Checker for Counter Systems

Demri

Finkel

Goranko

et al. 2006

Automated Technology for Verification and Analysis

View full text Add to dashboard Cite

Abstract. This paper deals with model-checking of fragments and extensions of CTL* on infinite-state Presburger counter systems, where the states are vectors of integers and the transitions are determined by means of relations definable within Presburger arithmetic. We have identified a natural class of admissible counter systems (ACS) for which we show that the quantification over paths in CTL* can be simulated by quantification over tuples of natural numbers, eventually allowing translation of the whole Presburger-CTL* into Presburger arithmetic, thereby enabling effective model checking. We have provided evidence that our results are close to optimal with respect to the class of counter systems described above. Finally, we design a complete semi-algorithm to verify first-order LTL properties over trace-flattable counter systems, extending the previous underlying FAST semi-algorithm to verify reachability questions over flattable counter systems.

show abstract

“…However, due to applications in the verification of infinite-state systems and other areas where infinite structures become increasingly important, it is interesting to study infinite arenas that admit some kind of finite presentation. The best studied class of such games are pushdown games [21,28], where the arena is the configuration graph of a pushdown automaton. Other relevant classes of infinite, but finitely presented, (game) graphs include prefix-recognizable graphs, HR-and VR-equational graphs, graphs in the Caucal hierarchy, and automatic graphs.…”

Section: Motivationmentioning

confidence: 99%

Positional Determinacy of Games with Infinitely Many Priorities

Grädel¹,

Walukiewicz²

2006

Logical Methods in Computer Science

Self Cite

View full text Add to dashboard Cite

Abstract. We study two-player games of infinite duration that are played on finite or infinite game graphs. A winning strategy for such a game is positional if it only depends on the current position, and not on the history of the play. A game is positionally determined if, from each position, one of the two players has a positional winning strategy.The theory of such games is well studied for winning conditions that are defined in terms of a mapping that assigns to each position a priority from a finite set C. Specifically, in Muller games the winner of a play is determined by the set of those priorities that have been seen infinitely often; an important special case are parity games where the least (or greatest) priority occurring infinitely often determines the winner. It is well-known that parity games are positionally determined whereas Muller games are determined via finite-memory strategies.In this paper, we extend this theory to the case of games with infinitely many priorities. Such games arise in several application areas, for instance in pushdown games with winning conditions depending on stack contents.For parity games there are several generalisations to the case of infinitely many priorities. While max-parity games over ω or min-parity games over larger ordinals than ω require strategies with infinite memory, we can prove that min-parity games with priorities in ω are positionally determined. Indeed, it turns out that the min-parity condition over ω is the only infinitary Muller condition that guarantees positional determinacy on all game graphs. MotivationThe problem of computing winning positions and winning strategies in infinite games has numerous applications in computing, most notably for the synthesis and verification of reactive controllers and for the model-checking of the µ-calculus and other logics. Of special importance are parity games, due to several reasons.

show abstract

Pushdown Processes: Games and Model Checking

Cited by 149 publications

References 10 publications

The Complexity of Model Checking Higher-Order Fixpoint Logic

The Complexity of Model Checking Higher-Order Fixpoint Logic

Towards a Model-Checker for Counter Systems

Positional Determinacy of Games with Infinitely Many Priorities

Contact Info

Product

Resources

About