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45
Pushdown Timed Automata: a Binary Reachability Characterization and Safety Verification
 Theoretical Computer Science
, 2003
"... We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachability ( ..."
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Cited by 21 (8 self)
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We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachability (i.e., the set of all pairs of configurations such that one can reach the other) of a PTA. Since a timed automaton can be treated as a PTA without the pushdown stack, we can show that the binary reachability of a timed automaton is definable in the additive theory of reals and integers. The results can be used to verify a class of properties containing linear relations over both dense variables and unbounded discrete variables. The properties previously could not be verified using the classic region technique nor expressed by timed temporal logics for timed automata and CTL for pushdown systems. The results are also extended to other generalizations of timed automata.
Parikh images of grammars: Complexity and applications
 IN LICS
, 2010
"... Parikh’s Theorem states that semilinear sets are effectively equivalent with the Parikh images of regular languages and those of contextfree languages. In this paper, we study the complexity of Parikh’s Theorem over any fixed alphabet size d. We prove various normal form theorems in the case of N ..."
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Cited by 20 (0 self)
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Parikh’s Theorem states that semilinear sets are effectively equivalent with the Parikh images of regular languages and those of contextfree languages. In this paper, we study the complexity of Parikh’s Theorem over any fixed alphabet size d. We prove various normal form theorems in the case of NFAs and CFGs. In particular, the normal form theorems ensure that a union of linear sets with d generators suffice to express such Parikh images, which in the case of NFAs can further be computed in polynomial time. We then apply apply our results to derive: (1) optimal complexity for decision problems concerning Parikh images (e.g. membership, universality, equivalence, and disjointness), (2) a new polynomial fragment of integer programming, (3) an answer to an open question about PAClearnability of semilinear sets, and (4) an optimal algorithm for verifying LTL over discretetimed reversalbounded counter systems.
Liveness verification of reversalbounded multicounter machines with a free counter
 In FSTTCS’01, volume 2245 of LNCS
, 2001
"... Abstract. We investigate the Presburger liveness problems for nondeterministicreversalbounded multicounter machines with a free counter (NCMFs). We show the following:The 9Presburgeri.o. problem and the 9Presburgereventual problem areboth decidable. So are their duals, the 8Presburgeralmost ..."
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Cited by 17 (8 self)
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Abstract. We investigate the Presburger liveness problems for nondeterministicreversalbounded multicounter machines with a free counter (NCMFs). We show the following:The 9Presburgeri.o. problem and the 9Presburgereventual problem areboth decidable. So are their duals, the 8Presburgeralmostalways problemand the 8Presburgeralways problem. The 8Presburgeri.o. problem and the 8Presburgereventual problem areboth undecidable. So are their duals, the 9Presburgeralmostalways problem and the 9Presburgeralways problem. These results can be used to formulate a weak form of Presburger linear temporal logic and develop its modelchecking theories for NCMFs. They can also be combined with [12] to study the same set of liveness problems on an extendedform of discrete timed automata containing, besides clocks, a number of reversalbounded counters and a free counter. 1 Introduction An infinitestate system can be obtained by augmenting a finite automaton with oneor more unbounded storage devices. The devices can be, for instance, counters (unary stacks), pushdown stacks, queues, and/or Turing tapes. However, an infinitestate system can easily achieve Turingcompleteness, e.g., when two counters are attached to a finite automaton (resulting in a &quot;Minsky machine&quot;). For these systems, even simpleproblems such as membership are undecidable.
Binary Reachability Analysis of Pushdown Timed Automata with Dense Clocks
 In CAV’01, volume 2102 of LNCS
"... . We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a control state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachab ..."
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Cited by 15 (10 self)
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. We consider pushdown timed automata (PTAs) that are timed automata (with dense clocks) augmented with a pushdown stack. A configuration of a PTA includes a control state, dense clock values and a stack word. By using the pattern technique, we give a decidable characterization of the binary reachability (i.e., the set of all pairs of configurations such that one can reach the other) of a PTA. Since a timed automaton can be treated as a PTA without the pushdown stack, we can show that the binary reachability of a timed automaton is definable in the additive theory of reals and integers. The results can be used to verify a class of properties containing linear relations over both dense variables and unbounded discrete variables. The properties previously could not be verified using the classic region technique nor expressed by timed temporal logics for timed automata and CTL for pushdown systems. 1 Introduction A timed automaton [3] can be considered as a finite automaton augmented...
Composability of infinitestate activity automata
, 2004
"... Abstract. Let be a class of (possibly nondeterministic) language acceptors with a oneway input tape. A system of automata in, is composable if for every string of symbols accepted by, there is an assignment of each symbol in to one of the ’s such that if is the subsequence assigned to, then is accep ..."
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Cited by 14 (3 self)
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Abstract. Let be a class of (possibly nondeterministic) language acceptors with a oneway input tape. A system of automata in, is composable if for every string of symbols accepted by, there is an assignment of each symbol in to one of the ’s such that if is the subsequence assigned to, then is accepted by. For a nonnegative integer, alookahead delegator for is a deterministic machine in which, knowing (a) the current states! of and the accessible “local ” information of each machine (e.g., the top of the stack if each machine is a pushdown automaton, whether a counter is zero on nonzero if each machine is a multicounter automaton, etc.), and (b) the lookahead symbols to the right of the current input symbol being processed, can uniquely determine " the to assign the current symbol. Moreover, every string accepted by is also accepted by, i.e., the subsequence of string delegated by to " each is accepted by. Thus,lookahead delegation is a stronger requirement than composability, since the delegator must be deterministic. A system that is composable may not have adelegator for any. We look at the decidability of composability and existence ofdelegators for various classes of machines. Our results have applications to automated composition of eservices. E
On Presburger Liveness of Discrete Timed Automata
 STACS'01, LNCS 2010
, 2001
"... Using an automatatheoretic approach, we investigate the decidabilityof liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburg ..."
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Cited by 13 (12 self)
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Using an automatatheoretic approach, we investigate the decidabilityof liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburger clock constraints is undecidable, we show that there are various classes of Presburgerliveness properties which are decidable for discrete timed automata. For instance, it is decidable, given a discrete timed automaton A and a Presburger property P,whether there exists an!path of A where P holds infinitely often. We also showthat other classes of Presburger liveness properties are indeed undecidable for discrete timed automata, e.g., whether P holds infinitely often for each!path of A. These results might give insights into the corresponding problems for timedautomata over dense domains, and help in the definition of a fragment of linear temporal logic, augmented with Presburger conditions on configurations, whichis decidable for model checking timed automata.
DenseTimed Pushdown Automata
"... Abstract—We propose a model that captures the behavior of realtime recursive systems. To that end, we introduce densetimed pushdown automata that extend the classical models of pushdown automata and timed automata, in the sense that the automaton operates on a finite set of realvalued clocks, and ..."
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Cited by 12 (4 self)
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Abstract—We propose a model that captures the behavior of realtime recursive systems. To that end, we introduce densetimed pushdown automata that extend the classical models of pushdown automata and timed automata, in the sense that the automaton operates on a finite set of realvalued clocks, and each symbol in the stack is equipped with a realvalued clock representing its “age”. The model induces a transition system that is infinite in two dimensions, namely it gives rise to a stack with an unbounded number of symbols each of which with a realvalued clock. The main contribution of the paper is an EXPTIMEcomplete algorithm for solving the reachability problem for densetimed pushdown automata. I.
Counter Machines and Verification Problems
, 2001
"... We study various generalizations of reversalbounded multicounter machines and show that they have decidable emptiness, infiniteness, disjointness, containment, and equivalence problems. The extensions include allowing the machines to perform linearrelation tests among the counters and parameterize ..."
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Cited by 12 (2 self)
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We study various generalizations of reversalbounded multicounter machines and show that they have decidable emptiness, infiniteness, disjointness, containment, and equivalence problems. The extensions include allowing the machines to perform linearrelation tests among the counters and parameterized constants (e.g., "Is 3x 5y 2D 1 +9D 2 < 12?", where x; y are counters, and D 1 ; D 2 are parameterized constants). We believe that these machines are the most powerful machines known to date for which these decision problems are decidable. Decidability results for such machines are useful in the analysis of reachability problems and the verification /debugging of safety properties in infinitestate transition systems. For example, we show that (binary, forward, and backward) reachability and safety are solvable for these machines.
Counter machines: decidable properties and applications to verification Problems
 MFCS'00, LNCS 1893
, 2000
"... Abstract. We study various generalizations of reversalbounded multicounter machines and show that they have decidable emptiness, infiniteness, disjointness, containment, and equivalence problems. The extensions include allowing the machines to perform linearrelation tests among the counters and pa ..."
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Cited by 9 (5 self)
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Abstract. We study various generalizations of reversalbounded multicounter machines and show that they have decidable emptiness, infiniteness, disjointness, containment, and equivalence problems. The extensions include allowing the machines to perform linearrelation tests among the counters and parameterized constants (e.g., “Is ¢¤£¦¥¨§�©�¥��¤���������������� �?”, where £¦�� © are counters, and �������� � are parameterized constants). We believe that these machines are the most powerful machines known to date for which these decision problems are decidable. Decidability results for such machines are useful in the analysis of reachability problems and the verification/debugging of safety properties in infinitestate transition systems. For example, we show that (binary, forward, and backward) reachability, safety, and invariance are solvable for these machines. 1
Presburger Liveness Verification of Discrete Timed Automata
, 2003
"... Using an automatatheoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburge ..."
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Cited by 8 (4 self)
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Using an automatatheoretic approach, we investigate the decidability of liveness properties (called Presburger liveness properties) for timed automata when Presburger formulas on configurations are allowed. While the general problem of checking a temporal logic such as TPTL augmented with Presburger clock constraints is undecidable, we show that there are various classes of Presburger liveness properties which are decidable for discrete timed automata. For instance, it is decidable, given a discrete timed automaton A and a Presburger property P , whether there exists an !path of A where P holds infinitely often. We also show that other classes of Presburger liveness properties are indeed undecidable for discrete timed automata, e.g., whether P holds infinitely often for each !path of A . These results might give insights into the corresponding problems for timed automata over dense domains, and help in the definition of a fragment of linear temporal logic, augmented with Presburger conditions on configurations, which is decidable for model checking timed automata.