A computerized workflow management system may enforce a security policy, specified in terms of authorized actions and constraints, thereby restricting which users can perform particular steps in a workflow. The existence of a security policy may mean it is impossible to find a valid plan (an assignment of steps to authorized users such that all constraints are satisfied). Work in the literature focuses on the workflow satisfiability problem, a problem that outputs a valid plan if the instance is satisfiable (and a negative result otherwise). In this paper, we introduce the ( ), which enables us to solve problems related to workflows and security policies. In particular, we are able to compute a "least bad" plan when some components of the security policy may be violated. In general, is intractable from both the classical and parameterized complexity point of view. We prove there exists an fixed-parameter tractable (FPT) algorithm to compute a Pareto front for if we restrict our attention to user-independent constraints. We also present a second algorithm to compute a Pareto front which uses mixed integer programming (MIP). We compare the performance of both our algorithms on synthetic instances, and show that the FPT algorithm outperforms the MIP-based one by several orders of magnitude on most of the instances. Finally, we study the important question of workflow resiliency and prove new results establishing that known decision problems are fixed-parameter tractable when restricted to user-independent constraints. We then propose a new way of modeling the availability of users and demonstrate that many questions related to resiliency in the context of this new model may be reduced to instances of .
A constraint @math is said to be (UI, for short) if, for every @math and every permutation @math , we have @math , where @math . Informally, a constraint is UI if it does not depend on the identity of the users. It appears most constraints that are useful in practice are UI @cite_19 . In particular, cardinality constraints, separation-of-duty and binding-of-duty constraints are UI. In our experiments (), we will consider two particular types of UI constraints: an constraint has the form @math , where @math , and is satisfied provided at least @math users are assigned to the steps in @math ; an constraint has the form @math , where @math , and is satisfied provided at most @math users are assigned to the steps in @math . Note that a separation-of-duty constraint @math is the counting constraint @math , and a binding-of-duty constraint @math is the constraint @math .
@cite_19
2949393806 2885396681 2531021157 2577171054
We show a new way to round vector solutions of semidefinite programming (SDP) hierarchies into integral solutions, based on a connection between these hierarchies and the spectrum of the input graph. We demonstrate the utility of our method by providing a new SDP-hierarchy based algorithm for constraint satisfaction problems with 2-variable constraints (2-CSP's). More concretely, we show for every 2-CSP instance I a rounding algorithm for r rounds of the Lasserre SDP hierarchy for I that obtains an integral solution that is at most worse than the relaxation's value (normalized to lie in [0,1]), as long as r > k ( ) ( ) ;, where k is the alphabet size of I, @math , and @math denotes the number of eigenvalues larger than @math in the normalized adjacency matrix of the constraint graph of @math . In the case that @math is a instance, the threshold @math is only a polynomial in @math , and is independent of the alphabet size. Also in this case, we can give a non-trivial bound on the number of rounds for instance. In particular our result yields an SDP-hierarchy based algorithm that matches the performance of the recent subexponential algorithm of Arora, Barak and Steurer (FOCS 2010) in the worst case, but runs faster on a natural family of instances, thus further restricting the set of possible hard instances for Khot's Unique Games Conjecture. Our algorithm actually requires less than the @math constraints specified by the @math level of the Lasserre hierarchy, and in some cases @math rounds of our program can be evaluated in time @math . We develop fast and memory efficient numerical methods for learning functions of many variables that admit sparse representations in terms of general bounded orthonormal tensor product bases. Such functions appear in many applications including, e.g., various Uncertainty Quantification(UQ) problems involving the solution of parametric PDE that are approximately sparse in Chebyshev or Legendre product bases. We expect that our results provide a starting point for a new line of research on sublinear-time solution techniques for UQ applications of the type above which will eventually be able to scale to significantly higher-dimensional problems than what are currently computationally feasible. More concretely, let @math be a finite Bounded Orthonormal Product Basis (BOPB) of cardinality @math . We will develop methods that approximate any function @math that is sparse in the BOPB, that is, @math of the form @math with @math of cardinality @math . Our method has a runtime of just @math , uses only @math function evaluations on a fixed and nonadaptive grid, and not more than @math bits of memory. For @math , the runtime @math will be less than what is required to simply enumerate the elements of the basis @math ; thus our method is the first approach applicable in a general BOPB framework that falls into the class referred to as "sublinear-time". This and the similarly reduced sample and memory requirements set our algorithm apart from previous works based on standard compressive sensing algorithms such as basis pursuit which typically store and utilize full intermediate basis representations of size @math . In our LICS 2004 paper we introduced an approach to the study of the local structure of finite algebras and relational structures that aims at applications in the Constraint Satisfaction Problem (CSP). This approach involves a graph associated with an algebra @math or a relational structure A, whose vertices are the elements of @math (or A), the edges represent subsets of @math such that the restriction of some term operation of @math is ‘good’ on the subset, that is, act as an operation of one of the 3 types: semilattice, majority, or affine. In this paper we significantly refine and advance this approach. In particular, we prove certain connectivity and rectangularity properties of relations over algebras related to components of the graph connected by semilattice and affine edges. We also prove a result similar to 2-decomposition of relations invariant under a majority operation, only here we do not impose any restrictions on the relation. These results allow us to give a new, somewhat more intuitive proof of the bounded width theorem: the CSP over algebra @math has bounded width if and only if @math does not contain affine edges. Actually, this result shows that bounded width implies width (2,3). We also consider algebras with edges from a restricted set of types. In particular, it can be proved that type restrictions are preserved under the standard algebraic constructions. Finally, we prove that algebras without semilattice edges have few subalgebras of powers, that is, the CSP over such algebras is also polynomial time. Difference constraints have been used for termination analysis in the literature, where they denote relational inequalities of the form @math xź≤y+c, and describe that the value of x in the current state is at most the value of y in the previous state plus some constant @math cźZ. We believe that difference constraints are also a good choice for complexity and resource bound analysis because the complexity of imperative programs typically arises from counter increments and resets, which can be modeled naturally by difference constraints. In this article we propose a bound analysis based on difference constraints. We make the following contributions: (1) our analysis handles bound analysis problems of high practical relevance which current approaches cannot handle: we extend the range of bound analysis to a class of challenging but natural loop iteration patterns which typically appear in parsing and string-matching routines. (2) We advocate the idea of using bound analysis to infer invariants: our soundness proven algorithm obtains invariants through bound analysis, the inferred invariants are in turn used for obtaining bounds. Our bound analysis therefore does not rely on external techniques for invariant generation. (3) We demonstrate that difference constraints are a suitable abstract program model for automatic complexity and resource bound analysis: we provide efficient abstraction techniques for obtaining difference constraint programs from imperative code. (4) We report on a thorough experimental comparison of state-of-the-art bound analysis tools: we set up a tool comparison on (a) a large benchmark of real-world C code, (b) a benchmark built of examples taken from the bound analysis literature and (c) a benchmark of challenging iteration patterns which we found in real source code. (5) Our analysis is more scalable than existing approaches: we discuss how we achieve scalability.