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Automata on guarded strings and applications
 Matématica Contemporânea
, 2001
"... Guarded strings are like ordinary strings over a finite alphabet P, except that atoms of the free Boolean algebra on a set of atomic tests B alternate with the symbols of P. The regular sets of guarded strings play the same role in Kleene algebra with tests as the regular sets of ordinary strings do ..."
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Guarded strings are like ordinary strings over a finite alphabet P, except that atoms of the free Boolean algebra on a set of atomic tests B alternate with the symbols of P. The regular sets of guarded strings play the same role in Kleene algebra with tests as the regular sets of ordinary strings do in Kleene algebra. In this paper we develop the elementary theory of finite automata on guarded strings, a generalization of the theory of finite automata on ordinary strings. We give several basic constructions, including determinization, state minimization, and an analog of Kleene’s theorem. We then use these results to verify a conjecture on the complexity of a complete Gentzenstyle sequent calculus for partial correctness. We also show that a basic result of the theory of Boolean decision diagrams (BDDs), namely that minimal ordered BDDs are unique, is a special case of the MyhillNerode theorem for a class of automata on guarded strings. 1
P.: A Constraint Store Based on Multivalued Decision Diagrams
 Principles and Practice of Constraint Programming (CP 2007). Lecture Notes in Computer Science
, 2007
"... Abstract. The typical constraint store transmits a limited amount of information because it consists only of variable domains. We propose a richer constraint store in the form of a limitedwidth multivalued decision diagram (MDD). It reduces to a traditional domain store when the maximum width is on ..."
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Abstract. The typical constraint store transmits a limited amount of information because it consists only of variable domains. We propose a richer constraint store in the form of a limitedwidth multivalued decision diagram (MDD). It reduces to a traditional domain store when the maximum width is one but allows greater pruning of the search tree for larger widths. MDD propagation algorithms can be developed to exploit the structure of particular constraints, much as is done for domain filtering algorithms. We propose specialized propagation algorithms for alldiff and inequality constraints. Preliminary experiments show that MDD propagation solves multiple alldiff problems an order of magnitude more rapidly than traditional domain propagation. It also significantly reduces the search tree for inequality problems, but additional research is needed to reduce the computation time. 1
Costbounded binary decision diagrams for 01 programming
 In: International Conference on Integration of AI and OR Techniques
, 2007
"... Abstract. In recent work binary decision diagrams (BDDs) were introduced as a technique for postoptimality analysis for integer programming. In this paper we show that much smaller BDDs can be used for the same analysis by employing cost bounding techniques in their construction. Binary decision dia ..."
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Abstract. In recent work binary decision diagrams (BDDs) were introduced as a technique for postoptimality analysis for integer programming. In this paper we show that much smaller BDDs can be used for the same analysis by employing cost bounding techniques in their construction. Binary decision diagrams (BDDs) have seen widespread application in logic circuit design and product configuration. They also have potential application to optimization, particularly to postoptimality analysis. A BDD can represent, often in compact form, the entire feasible set of an optimization problem. Optimal solutions correspond to shortest paths in the BDD. Due to the efficiency of this representation, one can rapidly extract a good deal of information about a problem and its solutions by querying the BDD. This opens the door to fast, indepth postoptimality analysis without having to resolve the problem repeatedly—provided the BDD is of manageable size. For instance, one can identify all optimal or nearoptimal solutions by finding all shortest or nearshortest paths in the BDD. One can quickly determine how
Postoptimality analysis for integer programming using binary decision diagrams
 Carnegie Mellon University
, 2006
"... We show how binary decision diagrams (BDDs) can be used to solve and obtain postoptimality analysis for linear and nonlinear integer programming problems with binary or general integer variables. A given constraint set corresponds to a unique reduced BDD that provides a potentially compact represent ..."
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We show how binary decision diagrams (BDDs) can be used to solve and obtain postoptimality analysis for linear and nonlinear integer programming problems with binary or general integer variables. A given constraint set corresponds to a unique reduced BDD that provides a potentially compact representation of all feasible or nearoptimal solutions. The BDD can be queried in real time for indepth postoptimality reasoning. The approach is equally effective for linear and nonlinear problems. There are currently no other methods for obtaining such an analysis, short of repeatedly resolving the problem. We illustrate the analysis on capital budgeting, network reliability, and portfolio design problems. 1
Typesafe modular hashconsing
 In: Proceedings of the 2006 workshop on ML
, 2006
"... Hashconsing is a technique to share values that are structurally equal. Beyond the obvious advantage of saving memory blocks, hashconsing may also be used to speed up fundamental operations and data structures by several orders of magnitude when sharing is maximal. This paper introduces an OCAML h ..."
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Cited by 11 (2 self)
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Hashconsing is a technique to share values that are structurally equal. Beyond the obvious advantage of saving memory blocks, hashconsing may also be used to speed up fundamental operations and data structures by several orders of magnitude when sharing is maximal. This paper introduces an OCAML hashconsing library that encapsulates hashconsed terms in an abstract datatype, thus safely ensuring maximal sharing. This library is also parameterized by an equality that allows the user to identify terms according to an arbitrary equivalence relation. D.2.3 [Software engineer
A BDDbased Model Checker for the PEP Tool
 Univ. of Newcastle, Dep. of CS, Major Individual Project
, 1997
"... PEP (Programming Environment based on Petri Nets) is a tool developed at the University of Hildesheim. It can be used for editing, simulating and verifying Petri nets, and for creating Petri nets from a program in an imperative programming language. For the verification task, model checkers are used ..."
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PEP (Programming Environment based on Petri Nets) is a tool developed at the University of Hildesheim. It can be used for editing, simulating and verifying Petri nets, and for creating Petri nets from a program in an imperative programming language. For the verification task, model checkers are used to decide whether a given logical formula is true or false for a particular Petri net. A fairly new method in implementing model checkers, symbolic model checking, involves binary decision diagrams (BDDs), a data structure for representing considerably large state spaces. In the individual project described in this dissertation, a BDDbased model checker for the PEP tool was developed that can verify safe Petri nets. The model checker makes use of the SMV system, developed at the Carnegie Mellon University. In addition, a range of different modelling possibilities, model checking options and optimisation techniques is discussed and evaluated using examples like the dining philosophers probl...
Inductive invariants for nested recursion
 Theorem Proving in Higher Order Logics (TPHOLS'03), volume 2758 of LNCS
, 2003
"... Abstract. We show that certain inputoutput relations, termed inductive invariants are of central importance for termination proofs of algorithms defined by nested recursion. Inductive invariants can be used to enhance recursive function definition packages in higherorder logic mechanizations. We d ..."
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Cited by 5 (2 self)
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Abstract. We show that certain inputoutput relations, termed inductive invariants are of central importance for termination proofs of algorithms defined by nested recursion. Inductive invariants can be used to enhance recursive function definition packages in higherorder logic mechanizations. We demonstrate the usefulness of inductive invariants on a large example of the BDD algorithm Apply. Finally, we introduce a related concept of inductive fixpoints with the property that for every functional in higherorder logic there exists a largest partial function that is such a fixpoint. 1
Essays on Equilibrium Computation, MDDbased Constraint Programming and Scheduling
, 2010
"... This thesis addresses three topics: solving the Nash Equilibrium problem for twoplayer zerosum games presented in extensive form, constraint programming using multivalued decision diagrams and scheduling cranes in a factory. In the first chapter, we develop a firstorder method based on a smoothin ..."
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This thesis addresses three topics: solving the Nash Equilibrium problem for twoplayer zerosum games presented in extensive form, constraint programming using multivalued decision diagrams and scheduling cranes in a factory. In the first chapter, we develop a firstorder method based on a smoothing technique of Nesterov that allows us to solve problems that are several orders of magnitude larger than was possible previously. The second chapter investigates constraint programming based on multivalued decision diagrams (MDDs). We present a systematic framework for designing filtering algorithms for MDDs as well as concrete instantiations for several different global constraints. We also discuss some ideas for primal heuristics and branching schemes using MDDs. The third chapter describes our implementation of a solver for constraint satisfaction problems where the domainstore has been replaced by MDDs. In the fourth chapter we present a case study of propagating among constraints using our framework and provide more evidence that MDDbased propagation can result in enormous reduction in the size of the search tree and solution time. In the final chapter of this thesis we address the problem of scheduling a pair of cranes that share a track to best follow a production schedule. We focus on the problem of solving the optimal control problem for
to appear. Decision diagrams and dynamic programming
 CPAIOR 2013 Proceedings
"... Abstract. Binary and multivalued decision diagrams are closely related to dynamic programming (DP) but differ in some important ways. This paper makes the relationship more precise by interpreting the DP state transition graph as a weighted decision diagram and incorporating the statedependent cost ..."
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Abstract. Binary and multivalued decision diagrams are closely related to dynamic programming (DP) but differ in some important ways. This paper makes the relationship more precise by interpreting the DP state transition graph as a weighted decision diagram and incorporating the statedependent costs of DP into the theory of decision diagrams. It generalizes a wellknown uniqueness theorem by showing that, for a given optimization problem and variable ordering, there is a unique reduced weighted decision diagram with “canonical ” edge costs. This can lead to simplification of DP models by transforming the costs to canonical costs and reducing the diagram, as illustrated by a standard inventory management problem. The paper then extends the relationship between decision diagrams and DP by introducing the concept of nonserial decision diagrams as a counterpart of nonserial dynamic programming. 1
Compactly generating all satisfying truth assignments of a Horn Formula
 Journal on Satisfiability, Boolean Modeling and Computation
"... While it was known that all models of a Horn formula can be generated in outputpolynomial time, here we present an explicit algorithm as opposed to the rather vague oraclescheme suggested in the proof of [6, Thm.4]. It is an instance of some principle of exclusion that compactly (thus not one by on ..."
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While it was known that all models of a Horn formula can be generated in outputpolynomial time, here we present an explicit algorithm as opposed to the rather vague oraclescheme suggested in the proof of [6, Thm.4]. It is an instance of some principle of exclusion that compactly (thus not one by one) generates all models of certain Boolean formulae given in CNF. The principle of exclusion can be adapted to generate only the models of weight k. We compare and contrast it with constraint programming, 0, 1 integer programming, and binary decision diagrams. Keywords: Hornmodels, outputpolynomial algorithm, fixedcardinality models