Branching Time Logics \mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha } with Operations Until and Since Based on Bundles of Integer Numbers, Logical Consecutions, Deciding Algorithms

This paper is intended as an attempt to describe logical consequence in branching time logics. We study temporal branching time logics $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ which use the standard operations Until and Next and dual operations Since and Previous (LTL, as standard, uses only Until and Next). Temporal logics $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ are generated by semantics based on Kripke/Hinttikka structures with linear frames of integer numbers $\mathcal {Z}$ with a single node (glued zeros). For $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ , the permissible branching of the node is limited by α (where 1≤α≤ω). We prove that any logic $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ is decidable w.r.t. admissible consecutions (inference rules), i.e. we find an algorithm recognizing consecutions admissible in $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ . As a consequence, it implies that $\mathcal {BTL}^{\mathrm {U,S}}_{\mathrm {N},\mathrm {N}^{-1}}(\mathcal {Z})_{\alpha }$ itself is decidable and solves the satisfiability problem.     

Delayed theory combination vs. Nelson-Oppen for satisfiability modulo theories: a comparative analysis

Most state-of-the-art approaches for Satisfiability Modulo Theories $(SMT(\mathcal{T}))$ rely on the integration between a SAT solver and a decision procedure for sets of literals in the background theory $\mathcal{T} (\mathcal{T}{\text {-}}solver)$ . Often $\mathcal{T}$ is the combination $\mathcal{T}_1 \cup \mathcal{T}_2$ of two (or more) simpler theories $(SMT(\mathcal{T}_1 \cup \mathcal{T}_2))$ , s.t. the specific ${\mathcal{T}_i}{\text {-}}solvers$ must be combined. Up to a few years ago, the standard approach to $SMT(\mathcal{T}_1 \cup \mathcal{T}_2)$ was to integrate the SAT solver with one combined $\mathcal{T}_1 \cup \mathcal{T}_2{\text {-}}solver$ , obtained from two distinct ${\mathcal{T}_i}{\text {-}}solvers$ by means of evolutions of Nelson and Oppen’s (NO) combination procedure, in which the ${\mathcal{T}_i}{\text {-}}solvers$ deduce and exchange interface equalities. Nowadays many state-of-the-art SMT solvers use evolutions of a more recent $SMT(\mathcal{T}_1 \cup \mathcal{T}_2)$ procedure called Delayed Theory Combination (DTC), in which each ${\mathcal{T}_i}{\text {-}}solver$ interacts directly and only with the SAT solver, in such a way that part or all of the (possibly very expensive) reasoning effort on interface equalities is delegated to the SAT solver itself. In this paper we present a comparative analysis of DTC vs. NO for $SMT(\mathcal{T}_1 \cup \mathcal{T}_2)$ . On the one hand, we explain the advantages of DTC in exploiting the power of modern SAT solvers to reduce the search. On the other hand, we show that the extra amount of Boolean search required to the SAT solver can be controlled. In fact, we prove two novel theoretical results, for both convex and non-convex theories and for different deduction capabilities of the ${\mathcal{T}_i}{\text {-}}solvers$ , which relate the amount of extra Boolean search required to the SAT solver by DTC with the number of deductions and case-splits required to the ${\mathcal{T}_i}{\text {-}}solvers$ by NO in order to perform the same tasks: (i) under the same hypotheses of deduction capabilities of the ${\mathcal{T}_i}{\text {-}}solvers$ required by NO, DTC causes no extra Boolean search; (ii) using ${\mathcal{T}_i}{\text {-}}solvers$ with limited or no deduction capabilities, the extra Boolean search required can be reduced down to a negligible amount by controlling the quality of the $\mathcal{T}$ -conflict sets returned by the ${\mathcal{T}_i}{\text {-}}solvers$ .     

Equiparadoxicality of Yablo’s Paradox and the Liar

It is proved that Yablo’s paradox and the Liar paradox are equiparadoxical, in the sense that their paradoxicality is based upon exactly the same circularity condition—for any frame ${\mathcal{K}}$ , the following are equivalent: (1) Yablo’s sequence leads to a paradox in ${\mathcal{K}}$ ; (2) the Liar sentence leads to a paradox in ${\mathcal{K}}$ ; (3) ${\mathcal{K}}$ contains odd cycles. This result does not conflict with Yablo’s claim that his sequence is non-self-referential. Rather, it gives Yablo’s paradox a new significance: his construction contributes a method by which we can eliminate the self-reference of a paradox without changing its circularity condition.     

Generalising Unit-Refutation Completeness and SLUR via Nested Input Resolution

The class ${\mathcal{SLUR}}$ (Single Lookahead Unit Resolution) was introduced in Schlipf et al. (Inf Process Lett 54:133–137, 1995) as an umbrella class for efficient (poly-time) SAT solving, with linear-time SAT decision, while the recognition problem was not considered. ?epek et al. (2012) and Balyo et al. (2012) extended this class in various ways to hierarchies covering all of CNF (all clause-sets). We introduce a hierarchy ${\mathcal{SLUR}}_k$ which we argue is the natural “limit” of such approaches. The second source for our investigations is the class ${\mathcal{UC}}$ of unit-refutation complete clause-sets, introduced in del Val (1994) as a target class for knowledge compilation. Via the theory of “hardness” of clause-sets as developed in Kullmann (1999), Kullmann (Ann Math Artif Intell 40(3–4):303–352, 2004) and Ansótegui et al. (2008) we obtain a natural generalisation ${\mathcal{UC}}_k$ , containing those clause-sets which are “unit-refutation complete of level k”, which is the same as having hardness at most k. Utilising the strong connections to (tree-)resolution complexity and (nested) input resolution, we develop basic methods for the determination of hardness (the level k in ${\mathcal{UC}}_k$ ). A fundamental insight now is that ${\mathcal{SLUR}}_k = {\mathcal{UC}}_k$ holds for all k. We can thus exploit both streams of intuitions and methods for the investigations of these hierarchies. As an application we can easily show that the hierarchies from ?epek et al. (2012) and Balyo et al. (2012) are strongly subsumed by ${\mathcal{SLUR}}_k$ . Finally we consider the problem of “irredundant” clause-sets in ${\mathcal{UC}}_k$ . For 2-CNF we show that strong minimisations are possible in polynomial time, while already for (very special) Horn clause-sets minimisation is NP-complete. We conclude with an extensive discussion of open problems and future directions. We envisage the concepts investigated here to be the starting point for a theory of good SAT translations, which brings together the good SAT-solving aspects from ${\mathcal{SLUR}}$ together with the knowledge-representation aspects from ${\mathcal{UC}}$ , and expands this combination via notions of “hardness”.     

Plaintext awareness in identity-based key encapsulation

The notion of plaintext awareness ( ${\mathsf{PA}}$ ) has many applications in public key cryptography: it offers unique, stand-alone security guarantees for public key encryption schemes, has been used as a sufficient condition for proving indistinguishability against adaptive chosen-ciphertext attacks ( ${\mathsf{IND}\hbox {-}{\mathsf{CCA}}}$ ), and can be used to construct privacy-preserving protocols such as deniable authentication. Unlike many other security notions, plaintext awareness is very fragile when it comes to differences between the random oracle and standard models; for example, many implications involving ${\mathsf{PA}}$ in the random oracle model are not valid in the standard model and vice versa. Similarly, strategies for proving ${\mathsf{PA}}$ of schemes in one model cannot be adapted to the other model. Existing research addresses ${\mathsf{PA}}$ in detail only in the public key setting. This paper gives the first formal exploration of plaintext awareness in the identity-based setting and, as initial work, proceeds in the random oracle model. The focus is laid mainly on identity-based key encapsulation mechanisms (IB-KEMs), for which the paper presents the first definitions of plaintext awareness, highlights the role of ${\mathsf{PA}}$ in proof strategies of ${\mathsf{IND}\hbox {-}{\mathsf{CCA}}}$ security, and explores relationships between ${\mathsf{PA}}$ and other security properties. On the practical side, our work offers the first, highly efficient, general approach for building IB-KEMs that are simultaneously plaintext-aware and ${\mathsf{IND}\hbox {-}{\mathsf{CCA}}}$ -secure. Our construction is inspired by the Fujisaki-Okamoto (FO) transform, but demands weaker and more natural properties of its building blocks. This result comes from a new look at the notion of $\gamma $ -uniformity that was inherent in the original FO transform. We show that for IB-KEMs (and PK-KEMs), this assumption can be replaced with a weaker computational notion, which is in fact implied by one-wayness. Finally, we give the first concrete IB-KEM scheme that is ${\mathsf{PA}}$ and ${\mathsf{IND}\hbox {-}{\mathsf{CCA}}}$ -secure by applying our construction to a popular IB-KEM and optimizing it for better performance.     

On the class of λ-statistically convergent difference sequences of fuzzy numbers

In this study, we introduce the sets $\left[ V,\lambda ,p\right] _{\Updelta }^{{\mathcal{F}}},\left[ C,1,p\right] _{\Updelta }^{{\mathcal{F}}}$ and examine their relations with the classes of $ S_{\lambda }\left( \Updelta ,{\mathcal{F}}\right)$ and $ S_{\mu }\left( \Updelta ,{\mathcal{F}}\right)$ of sequences for the sequences $\left( \lambda _{n}\right)$ and $\left( \mu _{n}\right) , 0<p<\infty $ and difference sequences of fuzzy numbers.     

Minimum Manhattan Network Problem in Normed Planes with Polygonal Balls: A Factor 2.5 Approximation Algorithm

Let ${\mathcal{B}}$ be a centrally symmetric convex polygon of ?² and ‖p?q‖ be the distance between two points p,q∈?² in the normed plane whose unit ball is ${\mathcal{B}}$ . For a set T of n points (terminals) in ?², a ${\mathcal{B}}$ -network on T is a network N(T)=(V,E) with the property that its edges are parallel to the directions of ${\mathcal{B}}$ and for every pair of terminals t _i and t _j , the network N(T) contains a shortest ${\mathcal{B}}$ -path between them, i.e., a path of length ‖t _i ?t _j ‖. A minimum ${\mathcal{B}}$ -network on T is a ${\mathcal{B}}$ -network of minimum possible length. The problem of finding minimum ${\mathcal{B}}$ -networks has been introduced by Gudmundsson, Levcopoulos, and Narasimhan (APPROX’99) in the case when the unit ball ${\mathcal{B}}$ is a square (and hence the distance ‖p?q‖ is the l ₁ or the l _∞-distance between p and q) and it has been shown recently by Chin, Guo, and Sun (Symposium on Computational Geometry, pp. 393–402, 2009) to be strongly NP-complete. Several approximation algorithms (with factors 8, 4, 3, and 2) for the minimum Manhattan problem are known. In this paper, we propose a factor 2.5 approximation algorithm for the minimum ${\mathcal{B}}$ -network problem. The algorithm employs a simplified version of the strip-staircase decomposition proposed in our paper (Chepoi et al. in Theor. Comput. Sci. 390:56–69, 2008, and APPROX-RANDOM, pp. 40–51, 2005) and subsequently used in other factor 2 approximation algorithms for the minimum Manhattan problem.     

Anti-unification for Unranked Terms and Hedges

We study anti-unification for unranked terms and hedges that may contain term and hedge variables. The anti-unification problem of two hedges ${\tilde{s}}_1$ and ${\tilde{s}}_2$ is concerned with finding their generalization, a hedge ${\tilde{q}}$ such that both ${\tilde{s}}_1$ and ${\tilde{s}}_2$ are instances of ${\tilde{q}}$ under some substitutions. Hedge variables help to fill in gaps in generalizations, while term variables abstract single (sub)terms with different top function symbols. First, we design a complete and minimal algorithm to compute least general generalizations. Then, we improve the efficiency of the algorithm by restricting possible alternatives permitted in the generalizations. The restrictions are imposed with the help of a rigidity function, which is a parameter in the improved algorithm and selects certain common subsequences from the hedges to be generalized. The obtained rigid anti-unification algorithm is further made more precise by permitting combination of hedge and term variables in generalizations. Finally, we indicate a possible application of the algorithm in software engineering.     

Integrated damping parameter and control design in structural systems for \bf{\mathcal{H}^2} and {\mathcal{H}^{\infty}} specifications

The paper presents a linear matrix inequality (LMI)-based approach for the simultaneous optimal design of output feedback control gains and damping parameters in structural systems with collocated actuators and sensors. The proposed integrated design is based on simplified $\mathcal{H}^2$ and $\mathcal{H}^{\infty}$ norm upper bound calculations for collocated structural systems. Using these upper bound results, the combined design of the damping parameters of the structural system and the output feedback controller to satisfy closed-loop $\mathcal{H}^2$ or $\mathcal{H}^{\infty}$ performance specifications is formulated as an LMI optimization problem with respect to the unknown damping coefficients and feedback gains. Numerical examples motivated from structural and aerospace engineering applications demonstrate the advantages and computational efficiency of the proposed technique for integrated structural and control design. The effectiveness of the proposed integrated design becomes apparent, especially in very large scale structural systems where the use of classical methods for solving Lyapunov and Riccati equations associated with $\mathcal{H}^2$ and $\mathcal{H}^{\infty}$ designs are time-consuming or intractable.     

On set consensus numbers

It is conjectured that the only way a failure detector (FD) can help solving n-process tasks is by providing k-set consensus for some ${k\in\{1,\ldots,n\}}$ among all the processes. It was recently shown by Zieli??ski that any FD that allows for solving a given n-process task that is unsolvable read-write wait-free, also solves (n ? 1)-set consensus. In this paper, we provide a generalization of Zieli??ski??s result. We show that any FD that solves a colorless task that cannot be solved read-write k-resiliently, also solves k-set consensus. More generally, we show that every colorless task ${\mathcal{T}}$ can be characterized by its set consensus number: the largest ${k\in\{1,\ldots,n\}}$ such that ${\mathcal{T}}$ is solvable (k ? 1)-resiliently. A task ${\mathcal{T}}$ with set consensus number k is, in the failure detector sense, equivalent to k-set consensus, i.e., a FD solves ${\mathcal{T}}$ if and only if it solves k-set consensus. As a corollary, we determine the weakest FD for solving k-set consensus in every environment, i.e., for all assumptions on when and where failures might occur.     

A representation of extra-special 2-group, entanglement, and Berry phase of two qubits in Yang-Baxter system

In this paper we show another representations of extra-special 2-groups. Based on this new representation, we infer a ${\mathbb{M}}$ matrix which obeys the extra-special 2-groups algebra relations. We also derive a unitary ${\breve{R}(\theta,\varphi)}$ matrix from the ${\mathbb{M}}$ using the Yang-Baxterization process. A Hamiltonian for the two qubits is constructed from the unitary ${\breve{R}(\theta,\varphi)}$ matrix. In this way, we study the Berry phase and entanglement of the two-qubit system. The results also establish relations between topological and holonomic quantum computation.     

An efficient simulation algorithm on Kripke structures

A number of algorithms for computing the simulation preorder (and equivalence) on Kripke structures are available. Let $\varSigma $ denote the state space, ${\rightarrow }$ the transition relation and $P_{\mathrm {sim}}$ the partition of $\varSigma $ induced by simulation equivalence. While some algorithms are designed to reach the best space bounds, whose dominating additive term is $|P_{\mathrm {sim}}|^2$ , other algorithms are devised to attain the best time complexity $O(|P_{\mathrm {sim}}||{\rightarrow }|)$ . We present a novel simulation algorithm which is both space and time efficient: it runs in $O(|P_ {\mathrm {sim}}|^2 \log |P_{\mathrm {sim}}| + |\varSigma |\log |\varSigma |)$ space and $O(|P_{\mathrm {sim}}||{\rightarrow }|\log |\varSigma |)$ time. Our simulation algorithm thus reaches the best space bounds while closely approaching the best time complexity.     

Tight Bounds for Distributed Minimum-Weight Spanning Tree Verification

This paper introduces the notion of distributed verification without preprocessing. It focuses on the Minimum-weight Spanning Tree (MST) verification problem and establishes tight upper and lower bounds for the time and message complexities of this problem. Specifically, we provide an MST verification algorithm that achieves simultaneously $\tilde{O}(m)$ messages and $\tilde{O}(\sqrt{n} + D)$ time, where m is the number of edges in the given graph G, n is the number of nodes, and D is G’s diameter. On the other hand, we show that any MST verification algorithm must send $\tilde{\varOmega}(m)$ messages and incur $\tilde{\varOmega}(\sqrt{n} + D)$ time in worst case. Our upper bound result appears to indicate that the verification of an MST may be easier than its construction, since for MST construction, both lower bounds of $\tilde{\varOmega}(m)$ messages and $\tilde{\varOmega}(\sqrt{n} + D)$ time hold, but at the moment there is no known distributed algorithm that constructs an MST and achieves simultaneously $\tilde{O}(m)$ messages and $\tilde{O}(\sqrt{n} + D)$ time. Specifically, the best known time-optimal algorithm (using ${\tilde{O}}(\sqrt {n} + D)$ time) requires O(m+n ^3/2) messages, and the best known message-optimal algorithm (using ${\tilde{O}}(m)$ messages) requires O(n) time. On the other hand, our lower bound results indicate that the verification of an MST is not significantly easier than its construction.     

Some properties of Rényi entropy over countably infinite alphabets

We study certain properties of Rényi entropy functionals $H_\alpha \left( \mathcal{P} \right)$ on the space of probability distributions over ?₊. Primarily, continuity and convergence issues are addressed. Some properties are shown to be parallel to those known in the finite alphabet case, while others illustrate a quite different behavior of the Rényi entropy in the infinite case. In particular, it is shown that for any distribution $\mathcal{P}$ and any r ∈ [0,∞] there exists a sequence of distributions $\mathcal{P}_n$ converging to $\mathcal{P}$ with respect to the total variation distance and such that $\mathop {\lim }\limits_{n \to \infty } \mathop {\lim }\limits_{\alpha \to 1 + } H_\alpha \left( {\mathcal{P}_n } \right) = \mathop {\lim }\limits_{\alpha \to 1 + } \mathop {\lim }\limits_{n \to \infty } H_\alpha \left( {\mathcal{P}_n } \right) + r$ .     

Cryptanalysis of Reduced-Round DASH

In ACISP 2008,the hash family DASH has been proposed by Billet et al.,which considers the design of Rijndael and RC6.DASH family has two variants that support 256-bit and 512-bit output length respectively.This paper presents the first third-party cryptanalysis of DASH-256 with a focus on the underlying block cipher A256.In particular,we study the distinguisher using differential and boomerang attack.As a result,we build a distinguishing attack for the compression function of DASH-256 with 8-round A256 using the differential cryptanalysis.Finally,we obtain a boomerang distinguisher of 9-round A256.     

Exact Algorithms for Finding Longest Cycles in Claw-Free Graphs

The Hamiltonian Cycle problem is the problem of deciding whether an n-vertex graph G has a cycle passing through all vertices of G. This problem is a classic NP-complete problem. Finding an exact algorithm that solves it in ${\mathcal {O}}^{*}(\alpha^{n})$ time for some constant α<2 was a notorious open problem until very recently, when Björklund presented a randomized algorithm that uses ${\mathcal {O}}^{*}(1.657^{n})$ time and polynomial space. The Longest Cycle problem, in which the task is to find a cycle of maximum length, is a natural generalization of the Hamiltonian Cycle problem. For a claw-free graph G, finding a longest cycle is equivalent to finding a closed trail (i.e., a connected even subgraph, possibly consisting of a single vertex) that dominates the largest number of edges of some associated graph H. Using this translation we obtain two deterministic algorithms that solve the Longest Cycle problem, and consequently the Hamiltonian Cycle problem, for claw-free graphs: one algorithm that uses ${\mathcal {O}}^{*}(1.6818^{n})$ time and exponential space, and one algorithm that uses ${\mathcal {O}}^{*}(1.8878^{n})$ time and polynomial space.     

New types of fuzzy ideals of near-rings

In this paper, we consider the $(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$ -fuzzy and $(\overline{\in}_{\gamma},\overline{\in}_{\gamma} \vee \; \overline{\hbox{q}}_{\delta})$ -fuzzy subnear-rings (ideals) of a near-ring. Some new characterizations are also given. In particular, we introduce the concepts of (strong) prime $(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$ -fuzzy ideals of near-rings and discuss the relationship between strong prime $(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$ -fuzzy ideals and prime $(\in_{\gamma},\in_{\gamma} \vee \; \hbox{q}_{\delta})$ -fuzzy ideals of near-rings.