Showing papers in "Information & Computation in 2017"

Exact algorithms for maximum independent set

Abstract: We show that the maximum independent set problem on an n-vertex graph can be solved in 1.1996 n n O ( 1 ) time and polynomial space, which even is faster than Robson's 1.2109 n n O ( 1 ) -time exponential-space algorithm published in 1986. We also obtain improved algorithms for MIS in graphs with maximum degree 6 and 7, which run in time of 1.1893 n n O ( 1 ) and 1.1970 n n O ( 1 ) , respectively. Our algorithms are obtained by using fast algorithms for MIS in low-degree graphs in a hierarchical way and making a careful analysis on the structure of bounded-degree graphs.

Mutual visibility by luminous robots without collisions

Abstract: We consider the Mutual Visibility problem for anonymous dimensionless robots with obstructed visibility moving in a plane: starting from distinct locations, the robots must reach, without colliding, a configuration where no three of them are collinear. We study this problem in the luminous robots model, in which each robot has a visible light that can assume colors from a fixed set.Among other results, we prove that Mutual Visibility can be solved in SSynch with 2 colors and in ASynch with 3 colors. If an adversary can interrupt and stop a robot moving to its computed destination, Mutual Visibility is still solvable in SSynch with 3 colors and, if the robots agree on the direction of one axis, also in ASynch.As a byproduct, we provide the first obstructed-visibility solutions to two classical problems for oblivious robots: collision-less convergence to a point (also known as near-gathering) and circle formation.

On the completeness of bounded model checking for threshold-based distributed algorithms

Abstract: Counter abstraction is a powerful tool for parameterized model checking, if the number of local states of the concurrent processes is relatively small. In recent work, we introduced parametric interval counter abstraction that allowed us to verify the safety and liveness of threshold-based fault-tolerant distributed algorithms (FTDA). Due to state space explosion, applying this technique to distributed algorithms with hundreds of local states is challenging for state-of-the-art model checkers. In this paper, we demonstrate that reachability properties of FTDAs can be verified by bounded model checking. To ensure completeness, we need an upper bound on the distance between states. We show that the diameters of accelerated counter systems of FTDAs, and of their counter abstractions, have a quadratic upper bound in the number of local transitions. Our experiments show that the resulting bounds are sufficiently small to use bounded model checking for parameterized verification of reachability properties of several FTDAs, some of which have not been automatically verified before.

The Calculus of Signal Flow Diagrams I

Abstract: We introduce a graphical syntax for signal flow diagrams based on the language of symmetric monoidal categories. Using universal categorical constructions, we provide a stream semantics and a sound and complete axiomatisation.A certain class of diagrams captures the orthodox notion of signal flow graph used in control theory; we show that any diagram of our syntax can be realised, via rewriting in the equational theory, as a signal flow graph.

Undecidability of asynchronous session subtyping

Abstract: Session types are used to describe communication protocols in distributed systems and, as usual in type theories, session subtyping characterizes substitutability of the communicating processes. We investigate the (un)decidability of subtyping for session types in asynchronously communicating systems. We first devise a core undecidable subtyping relation that is obtained by imposing limitations on the structure of types. Then, as a consequence of this initial undecidability result, we show that (differently from what stated or conjectured in the literature) the three notions of asynchronous subtyping defined so far for session types are all undecidable. Namely, we consider the asynchronous session subtyping by Mostrous and Yoshida for binary sessions, the relation by Chen et al. for binary sessions under the assumption that every message emitted is eventually consumed, and the one by Mostrous et al. for multiparty session types. Finally, by showing that two fragments of the core subtyping relation are decidable, we evince that further restrictions on the structure of types make our core subtyping relation decidable.

Gathering of oblivious robots on infinite grids with minimum traveled distance

Abstract: A largely studied version of the gathering problem asks to move a set of robots initially placed at different vertices of an anonymous graph toward a common vertex, and to let them remain at such a vertex. Asynchronous robots move based on the so-called Look–Compute–Move model. Each time a robot wakes-up, it perceives the current configuration in terms of occupied vertices (Look), it decides whether to move toward one of its neighbors (Compute), and then it performs the computed move (Move), eventually. So far, the main goal has been to detect the minimal assumptions that allow to accomplish the task, without taking care of any cost measure. In this paper, we are interested in optimal algorithms in terms of total number of moves. We consider infinite grids, and we fully characterize when optimal gathering is achievable by providing a distributed algorithm.

Deadlock analysis of unbounded process networks

Abstract: Deadlock detection in concurrent programs that create networks with arbitrary numbers of nodes is extremely complex and solutions either give imprecise answers or do not scale. To enable the analysis of such programs, (1) we define an algorithm for detecting deadlocks of a basic model featuring recursion and fresh name generation: the lam programs, and (2) we design a type system for value-passing CCS that returns lam programs. We show the soundness of the type system, and develop a type inference algorithm for it. The resulting algorithm is able to check deadlock-freedom of programs that cannot be handled by previous analyses, such as those that build unbounded networks.

Deeper local search for parameterized and approximation algorithms for maximum internal spanning tree

Abstract: The maximum internal spanning tree problem asks for a spanning tree of a given graph that has the maximum number of internal vertices among all spanning trees of this graph. In its parameterized version, we are interested in whether the graph has a spanning tree with at least k internal vertices. Fomin et al. (2013) 4 crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a 3k-vertex kernel, implying an O * ( 8 k ) -time parameterized algorithm. Using depth-2 local search, Knauer and Spoerhase (2015) 9 developed a (5/3)-approximation algorithm for the optimization version. We try deeper local search: We conduct a thorough combinatorial analysis on the obtained spanning trees and explore their algorithmic consequences. We first observe that from the spanning tree obtained by depth-3 local search, one can easily find a reducible structure and apply the reduction rule of Fomin et al. This gives an improved kernel of 2k vertices, and as a by-product, a deterministic algorithm running in time O * ( 4 k ) . We then go even deeper by considering the spanning tree obtained by depth-5 local search. It is shown that the number of internal vertices of this spanning tree is at least 2/3 of the maximum number a spanning tree can have, thereby delivering an improved approximation algorithm with ratio 1.5 for the problem.

Petri games: Synthesis of distributed systems with causal memory

Abstract: We present a new multiplayer game model for the interaction and the flow of information in a distributed system. The players are tokens on a Petri net. As long as the players move in independent parts of the net, they do not know of each other; when they synchronize at a joint transition, each player gets informed of the causal history of the other player. We show that for Petri games with a single environment player and an arbitrary bounded number of system players, deciding the existence of a safety strategy for the system players is EXPTIME-complete.

A decomposition theorem and two algorithms for reticulation-visible networks

Abstract: In studies of molecular evolution, phylogenetic trees are rooted binary trees, whereas phylogenetic networks are rooted acyclic digraphs. Edges are directed away from the root and leaves are uniquely labeled with taxa in phylogenetic networks. For the purpose of validating evolutionary models, biologists check whether or not a phylogenetic tree (resp. cluster) is contained in a phylogenetic network on the same taxa. These tree and cluster containment problems are known to be NP-complete. A phylogenetic network is reticulation-visible if every reticulation node separates the root of the network from at least a leaf. We answer an open problem by proving that the tree containment problem is solvable in quadratic time for reticulation-visible networks. The key tool used in our answer is a powerful decomposition theorem. It also allows us to design a linear-time algorithm for the cluster containment problem for networks of this type and to prove that every galled network with n leaves has 2 ( n - 1 ) reticulation nodes at most.

Meet your expectations with guarantees: Beyond worst-case synthesis in quantitative games

Abstract: Classical analysis of two-player quantitative games involves an adversary (modeling the environment of the system) which is purely antagonistic and asks for strict guarantees while Markov decision processes model systems facing a purely randomized environment: the aim is then to optimize the expected payoff, with no guarantee on individual outcomes. We introduce the beyond worst-case synthesis problem, which is to construct strategies that guarantee some quantitative requirement in the worst-case while providing a higher expected value against a particular stochastic model of the environment given as input. We study the beyond worst-case synthesis problem for two important quantitative settings: the mean-payoff and the shortest path. In both cases, we show how to decide the existence of finite-memory strategies satisfying the problem and how to synthesize one if one exists. We establish algorithms and we study complexity bounds and memory requirements.

Online algorithms with advice: The tape model

Abstract: We investigate to what extent the solution quality of online algorithms can be improved when supplying them with information about the input. To this end, we refine the recently introduced notion of advice complexity where the algorithm has access to an advice string that is communicated by an oracle with access to the complete input. The advice complexity is the length of this communication. We study the connections between advice complexity and both determinism and randomization using the paging problem, job shop scheduling, and a routing problem as sample problems. Our results for these problems show that very small advice (only three bits in the case of paging) suffices to significantly improve over the best deterministic algorithms. To be as good as randomized algorithms, a moderate number of advice bits is sufficient, but it varies with the specific problem considered. However, to obtain optimality, usually very large advice is necessary.

Parametric Linear Dynamic Logic

Abstract: We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by adding temporal operators equipped with parameters that bound their scope. LDL is an extension of Linear Temporal Logic (LTL) to all ω-regular specifications, while maintaining a translation into exponentially-sized non-deterministic Buchi automata. Since LDL cannot express timing constraints, we add parameterized operators and subsume parameterized extensions of LTL like Parametric LTL and PROMPT-LTL. Our contribution is a translation of PLDL into exponentially-sized non-deterministic Buchi automata via alternating automata. This yields PSPACE algorithms for model checking and assume-guarantee model checking and a 2EXPTIME realizability algorithm. The problems are complete for their complexity classes. We give tight bounds on optimal parameter values for model checking and realizability and present a PSPACE procedure for model checking optimization and a 3EXPTIME algorithm for realizability optimization. Our results show that these PLDL problems are no harder than their (parametric) LTL counterparts.

Complexity of validity for propositional dependence logics

Abstract: We study the complexity of the validity problems of propositional dependence logic, modal dependence logic, and extended modal dependence logic. We show that the validity problem for propositional dependence logic is NEXPTIME -complete. In addition, we establish that the corresponding problems for modal dependence logic and extended modal dependence logic coincide. We show containment in NEXPTIME NP , whereas NEXPTIME -hardness follows from the propositional case.

The vectorial λ-calculus

Abstract: We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed λ-calculus is strongly normalising and features weak subject reduction. Finally, we show how to naturally encode matrices and vectors in this typed calculus.

Quantitative model-checking of controlled discrete-time Markov processes☆

Abstract: This paper focuses on optimizing probabilities of events of interest defined over general controlled discrete-time Markov processes. It is shown that the optimization over a wide class of ω-regular properties can be reduced to the solution of one of two fundamental problems: reachability and repeated reachability. We provide a comprehensive study of the former problem and an initial characterization of the (much more involved) latter problem. A case study elucidates concepts and techniques.

Unit interval editing is fixed-parameter tractable

Abstract: Given a graph G and integers k 1 , k 2 , and k 3 , the unit interval editing problem asks whether G can be transformed into a unit interval graph by at most k 1 vertex deletions, k 2 edge deletions, and k 3 edge additions. We give an algorithm solving this problem in time 2 O ( k log ⁡ k ) ⋅ ( n + m ) , where k : = k 1 + k 2 + k 3 , and n , m denote respectively the numbers of vertices and edges of G. Therefore, it is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm implies the fixed-parameter tractability of the unit interval edge deletion problem, for which we also present a more efficient algorithm running in time O ( 4 k ⋅ ( n + m ) ) . Another result is an O ( 6 k ⋅ ( n + m ) ) -time algorithm for the unit interval vertex deletion problem, significantly improving the algorithm of van 't Hof and Villanger, which runs in time O ( 6 k ⋅ n 6 ) .

Complexity of Universality and Related Problems for Partially Ordered NFAs

Abstract: Partially ordered NFAs (poNFAs) are NFAs where cycles occur only in the form of self-loops. A poNFA is universal if it accepts all words over its alphabet. Deciding universality is PSpace -complete for poNFAs. We show that this remains true when restricting to fixed alphabets. This is nontrivial since standard encodings of symbols in, e.g., binary can turn self-loops into longer cycles. A lower coNP -complete complexity bound is obtained if all self-loops in the poNFA are deterministic. We find that such restricted poNFAs (rpoNFAs) characterize R -trivial languages, and establish the complexity of deciding if the language of an NFA is R -trivial. The limitation to fixed alphabets is essential even in the restricted case: deciding universality of rpoNFAs with unbounded alphabets is PSpace -complete. Consequently, we obtain the complexity results for inclusion and equivalence problems. Finally, we show that the languages of rpoNFAs are definable by deterministic (one-unambiguous) regular expressions.

Characterisation of the state spaces of marked graph Petri nets

Abstract: The structure of the reachability graph of a marked graph Petri net is fully characterised. Exact structural conditions are given for a given labelled transition system to be generated by a marked graph. Two cases are distinguished, corresponding to the boundedness or the unboundedness of the net, and, respectively, to the finiteness or the infiniteness of the transition system. Dedicated synthesis procedures are presented for both cases, and it is shown that there is always a unique minimal solution. The synthesis procedures allow this minimal net, its initial marking, and the marking bounds of its places to be computed from the labelled transition system.

The complexity of data aggregation in static and dynamic wireless sensor networks

Abstract: The contribution of this paper is threefold. First, we give tight bounds for the complexity of the problem of data aggregation in static networks. In more details, we show that the problem remains NP-complete when the graph is of degree at most three. Second, we investigate the complexity of the same problem in a dynamic network, that is, a network whose topology can evolve through time. In the case of dynamic networks, we show that the problem is NP-complete even in the case where the graph is of degree at most two. Third, we give the first lower and upper bounds for the minimum data aggregation time in a dynamic graph. We also observe that even in a well-connected evolving graphs, the optimal solution cannot be found by a distributed algorithm or by a centralized algorithm that does not know the future.

Zero knowledge and circuit minimization

Abstract: We show that every problem in the complexity class SZK (Statistical Zero Knowledge) is efficiently reducible to the Minimum Circuit Size Problem (MCSP). In particular Graph Isomorphism lies in RP MCSP .

Model theory of XPath on data trees. Part II: Binary bisimulation and definability

Abstract: We study the expressive power of the downward and vertical fragments of XPath equipped with (in)equality tests over possibly infinite data trees. We introduce a suitable notion of saturation with respect to node expressions, and show that over saturated data trees, the already studied notion of (unary) bisimulation coincides with the idea of ‘indistinguishability by means of node expressions’. We also prove definability and separation theorems for classes of pointed data trees. We introduce new notions of binary bisimulations, which relate two pairs of nodes of data trees. We show that over finitely branching data trees, these notions correspond to the idea of ‘indistinguishability by means of path expressions’. We prove a characterization theorem, which describes when a first-order formula with two free variables is expressible in the downward fragment. We show definability and separation theorems, for classes of two-pointed data trees and in the context of path expressions.

A procedure for deciding symbolic equivalence between sets of constraint systems

Abstract: We consider security properties of cryptographic protocols that can be modelled using trace equivalence, a crucial notion when specifying privacy-type properties, like anonymity, vote-privacy, and unlinkability. Infinite sets of possible traces are symbolically represented using deducibility constraints. We describe an algorithm that decides trace equivalence for protocols that use standard primitives and that can be represented using such constraints. More precisely, we consider symbolic equivalence between sets of constraint systems, and we also consider disequations. Considering sets and disequations is actually crucial to decide trace equivalence for processes that may involve else branches and/or private channels (for a bounded number of sessions). Our algorithm for deciding symbolic equivalence between sets of constraint systems is implemented and performs well in practice. Unfortunately, it does not scale up well for deciding trace equivalence between processes. This is however the first implemented algorithm deciding trace equivalence on such a large class of processes.

Automata for regular expressions with shuffle

Abstract: We generalize the partial derivative automaton and the position automaton to regular expressions with shuffle, and study their state complexity in the worst, as well as in the average case. The number of states of the partial derivative automaton ( A p d ) is, in the worst case, at most 2 m , where m is the number of letters in the expression. The asymptotic average is bounded by ( 4 3 ) m . We define a position automaton ( A p o s ) that is homogeneous, but in which several states can correspond to a same position, and we show that A p d is a quotient of A p o s . The number of states of the position automaton is at most 1 + m ( 2 m − 1 ) , while the asymptotic average is no more than m ( 4 3 ) m .

Exact algorithms for Maximum Induced Matching

Abstract: This paper studies exact algorithms for the Maximum Induced Matching problem, in which an n-vertex graph is given and we are asked to find a set of maximum number of edges in the graph such that no pair of edges in the set have a common endpoint or are adjacent by another edge. This problem has applications in many different areas. We give several structural properties of the problem and show that the problem can be solved in O⁎(1.4231n) time and polynomial space or O⁎(1.3752n) time and exponential space.

An efficient time-free solution to QSAT problem using P systems with proteins on membranes

Abstract: P systems are a class of distributed parallel computing devices inspired by some basic behaviors of biological membranes, which have the restriction that each rule is executed in exactly one time unit. However, it is natural to consider the systems without the time restriction on each rule since biochemical reactions in biological systems are inherently parallel and have different reaction rates, and the execution time of biochemical reactions is unpredictably sensitive to environmental factors. In this work, we construct a family of P systems with proteins on membranes and membrane division that are “robust” against the execution time of rules. Specifically, we present a time-free uniform solution to the QSAT problem by using P systems with proteins on membranes and membrane division in the sense that the execution time of the involved rules has no influence on the correctness of the solution.

Reaching approximate Byzantine consensus with multi-hop communication☆

Abstract: We are interested in approximate Byzantine consensus problem, wherein all the fault-free processes reach consensus asymptotically (approximately in finite time). In particular, we focus on the algorithms under which each process communicates with other processes that are up to l hops away and maintains minimal states across iterations. For a given l, we identify a necessary and sufficient condition on the network structure for the existence of iterative algorithms of interest. Our necessary and sufficient condition generalizes the tight condition identified in prior work for l = 1 . For l ≥ l ⁎ , where l ⁎ is the length of a longest cycle-free path in the given network, our condition is equivalent to the necessary and sufficient conditions for exact consensus in undirected and directed networks both.

Modeling concurrency with interval traces

Abstract: Interval order structures are useful tools to model abstract concurrent histories, i.e. sets of equivalent system runs, when system runs are modeled with interval orders. This paper shows how interval order structures can be modeled by partially commutative monoids, called interval traces. The model is then used to provide a semantics of Petri nets with inhibitor arcs, both in terms of interval traces and in terms of interval order structures.

FPT approximation schemes for maximizing submodular functions

Abstract: We investigate the existence of approximation algorithms for maximization of submodular functions, that run in a fixed parameter tractable (FPT) time. Given a non-decreasing submodular set function v : 2 X → R the goal is to select a subset S of K elements from X such that v ( S ) is maximized. We identify three properties of set functions, referred to as p-separability properties, and we argue that many real-life problems can be expressed as maximization of submodular, p-separable functions, with low values of the parameter p. We present FPT approximation schemes for the minimization and maximization variants of the problem, for several parameters that depend on characteristics of the optimized set function, such as p and K.

Self-Stabilizing Leader Election in Polynomial Steps

Abstract: We propose a silent self-stabilizing leader election algorithm for bidirectional arbitrary connected identified networks. This algorithm is written in the locally shared memory model under the distributed unfair daemon. It requires no global knowledge on the network. Its stabilization time is in Θ ( n 3 ) steps in the worst case, where n is the number of processes. Its memory requirement is asymptotically optimal, i.e., Θ ( log ⁡ n ) bits per processes. Its round complexity is of the same order of magnitude — i.e., Θ ( n ) rounds — as the best existing algorithms designed with similar settings. To the best of our knowledge, this is the first self-stabilizing leader election algorithm for arbitrary identified networks that is proven to achieve a stabilization time polynomial in steps. By contrast, we show that the previous best existing algorithms designed with similar settings stabilize in a non-polynomial number of steps in the worst case.