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258
Derivation Tree Analysis for Accelerated FixedPoint Computation
"... Abstract. We show that for several classes of idempotent semirings the least fixedpoint of a polynomial system of equations X = f(X) is equal to the least fixedpoint of a linear system obtained by “linearizing ” the polynomials of f in a certain way. Our proofs rely on derivation tree analysis, a ..."
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Cited by 3 (3 self)
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point. We use these algorithms to derive several consequences, including an O(N 3) algorithm for computing the throughput of a contextfree grammar (obtained by speeding up the O(N 4) algorithm of [2]), and a generalization of Courcelle’s result stating that the downwardclosed image of a context
Dependently Typed Functional Programs and their Proofs
, 1999
"... Research in dependent type theories [ML71a] has, in the past, concentrated on its use in the presentation of theorems and theoremproving. This thesis is concerned mainly with the exploitation of the computational aspects of type theory for programming, in a context where the properties of programs ..."
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Cited by 85 (13 self)
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Research in dependent type theories [ML71a] has, in the past, concentrated on its use in the presentation of theorems and theoremproving. This thesis is concerned mainly with the exploitation of the computational aspects of type theory for programming, in a context where the properties of programs may readily be specified and established. In particular, it develops technology for programming with dependent inductive families of datatypes and proving those programs correct. It demonstrates the considerable advantage to be gained by indexing data structures with pertinent characteristic information whose soundness is ensured by typechecking, rather than human effort. Type theory traditionally presents safe and terminating computation on inductive datatypes by means of elimination rules which serve as induction principles and, via their associated reduction behaviour, recursion operators [Dyb91]. In the programming language arena, these appear somewhat cumbersome and give rise to unappealing code, complicated by the inevitable interaction between case analysis on dependent types and equational reasoning on their indices which must appear explicitly in the terms. Thierry Coquand’s proposal [Coq92] to equip type theory directly with the kind of
OntheFly Analysis of Systems with Unbounded, Lossy FIFO Channels
 In CAV'98. LNCS 1427
, 1998
"... . We consider symbolic onthefly verification methods for systems of finitestate machines that communicate by exchanging messages via unbounded and lossy FIFO queues. We propose a novel representation formalism, called simple regular expressions (SREs), for representing sets of states of proto ..."
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Cited by 81 (19 self)
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. We consider symbolic onthefly verification methods for systems of finitestate machines that communicate by exchanging messages via unbounded and lossy FIFO queues. We propose a novel representation formalism, called simple regular expressions (SREs), for representing sets of states of protocols with lossy FIFO channels. We show that the class of languages representable by SREs is exactly the class of downward closed languages that arise in the analysis of such protocols. We give methods for (i) computing inclusion between SREs, (ii) an SRE representing the set of states reachable by executing a single transition in a system, and (iii) an SRE representing the set of states reachable by an arbitrary number of executions of a control loop of a program. All these operations are rather simple and can be carried out in polynomial time. With these techniques, one can construct a semialgorithm which explores the set of reachable states of a protocol, in order to check variou...
FORWARD ANALYSIS FOR WSTS, PART I: COMPLETIONS
, 2009
"... Wellstructured transition systems provide the right foundation to compute a finite basis of the set of predecessors of the upward closure of a state. The dual problem, to compute a finite representation of the set of successors of the downward closure of a state, is harder: Until now, the theoretic ..."
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Cited by 19 (9 self)
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, the theoretical framework for manipulating downwardclosed sets was missing. We answer this problem, using insights from domain theory (dcpos and ideal completions), from topology (sobrifications), and shed new light on the notion of adequate domains of limits.
Dynamic Data Mining: Exploring Large Rule Spaces by Sampling
, 1998
"... A great challenge for data mining techniques is the huge space of potential rules which can be generated. If there are tens of thousands of items, then potential rules involving three items number in the trillions. Traditional data mining techniques rely on downwardclosed measures such as support t ..."
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Cited by 7 (1 self)
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A great challenge for data mining techniques is the huge space of potential rules which can be generated. If there are tens of thousands of items, then potential rules involving three items number in the trillions. Traditional data mining techniques rely on downwardclosed measures such as support
On the decidability of metric temporal logic
 In Proc. LICS
, 2005
"... Metric Temporal Logic (MTL) is a prominent specification formalism for realtime systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with nonprimitive recursive complexity. We also consider the modelchecking problem for MTL: whether all w ..."
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Cited by 68 (11 self)
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Metric Temporal Logic (MTL) is a prominent specification formalism for realtime systems. In this paper, we show that the satisfiability problem for MTL over finite timed words is decidable, with nonprimitive recursive complexity. We also consider the modelchecking problem for MTL: whether all words accepted by a given AlurDill timed automaton satisfy a given MTL formula. We show that this problem is decidable over finite words. Over infinite words, we show that model checking the safety fragment of MTL—which includes invariance and timebounded response properties—is also decidable. These results are quite surprising in that they contradict various claims to the contrary that have appeared in the literature. The question of the decidability of MTL over infinite words remains open. 1.
Submitted to the Symposium on Theoretical Aspects of Computer Science www.stacsconf.org FORWARD ANALYSIS FOR WSTS, PART I: COMPLETIONS
"... ABSTRACT. Wellstructured transition systems provide the right foundation to compute a finite basis of the set of predecessors of the upward closure of a state. The dual problem, to compute a finite representation of the set of successors of the downward closure of a state, is harder: Until now, the ..."
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, the theoretical framework for manipulating downwardclosed sets was missing. We answer this problem, using insights from domain theory (dcpos and ideal completions), from topology (sobrifications), and shed new light on the notion of adequate domains of limits. 1.
www.stacsconf.org FORWARD ANALYSIS FOR WSTS, PART I: COMPLETIONS
, 2009
"... ABSTRACT. Wellstructured transition systems provide the right foundation to compute a finite basis of the set of predecessors of the upward closure of a state. The dual problem, to compute a finite representation of the set of successors of the downward closure of a state, is harder: Until now, the ..."
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, the theoretical framework for manipulating downwardclosed sets was missing. We answer this problem, using insights from domain theory (dcpos and ideal completions), from topology (sobrifications), and shed new light on the notion of adequate domains of limits. 1.
The Theory of Timed I/O Automata
, 2003
"... This paper presents the Timed Input/Output Automaton (TIOA) modeling framework, a basic mathematical framework to support description and analysis of timed systems. An important feature of this model is its support for decomposing timed system descriptions. In particular, the framework includes a no ..."
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Cited by 63 (29 self)
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This paper presents the Timed Input/Output Automaton (TIOA) modeling framework, a basic mathematical framework to support description and analysis of timed systems. An important feature of this model is its support for decomposing timed system descriptions. In particular, the framework includes a notion of external behavior for a timed I/O automaton, which captures its discrete interactions with its environment. The framework also denes what it means for one TIOA to implement another, based on an inclusion relationship between their external behavior sets, and de nes notions of simulations, which provide sucient conditions for demonstrating implementation relationships. The framework includes a composition operation for TIOAs, which respects external behavior, and a notion of receptiveness, which implies that a TIOA does not block the passage of time. The TIOA framework supports the statement and verication of safety and liveness properties for timed systems. It denes what it means for a property to be a safety or a liveness property, includes basic results about safetyliveness classication, and
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