An algebraic axiomatization of the Ewald’s intuitionistic tense logic

Ewald (J Symbolic Logic 51(1):166–179, 1986) considered tense operators \(G\) , \(H\) , \(F\) and \(P\) on intuitionistic propositional calculus and constructed an intuitionistic tense logic system called IKt. The aim of this paper is to give an algebraic axiomatization of the IKt system. We will also show that the algebraic axiomatization given by Chajda (Cent Eur J Math 9(5):1185–1191, 2011) of the tense operators \(P\) and \(F\) in intuitionistic logic is not in accordance with the Halmos definition of existential quantifiers. In this paper, we will study the IKt variety of IKt-algebras. First, we will introduce some examples and we will prove some properties. Next, we will prove that the IKt system has IKt-algebras as algebraic counterpart. We will also describe a discrete duality for IKt-algebras bearing in mind the results indicated by Or?owska and Rewitzky (Fundam Inform 81(1–3):275–295, 2007) for Heyting algebras. We will also get a general construction of tense operators on a complete Heyting algebra, which is a power lattice via the so-called Heyting frame. Finally, we will introduce the notion of tense deductive system which allowed us both to determine the congruence lattice in an IKt-algebra and to characterize simple and subdirectly irreducible algebras of the IKt variety.     

A propositional probabilistic logic with discrete linear time for reasoning about evidence

The aim of the paper is to present a sound, strongly complete and decidable probabilistic temporal logic that can model reasoning about evidence. The formal system developed here is actually a solution of a problem proposed by Halpern and Pucella (J Artif Intell Res 26:1–34, 2006).     

Asymptotic spectral distributions of Manhattan products of C_{n}\sharp P_{m}

The Manhattan product of directed cycles \(C_{n}\) and directed paths \(P_{m}\) is a diagraph. Recently, in quantum probability theory, several authors have studied the spectrum of graph, as mentioned also by A. Hora and N. Obata. In the paper, we study asymptotic spectral distribution of the Manhattan products of simple digraphs- \(C_{n}\sharp P_{m}\) . The limit of the spectral distribution of \(C_{n}\sharp P_{2}\) as \(n\rightarrow \infty \) exists in the sense of weak convergence, and its concrete form is obtained. We insist on the fact that this note does not contain any new results, which is only some parallel results with Obata (Interdiscip Inf Sci 18(1):43–54, 2012) or Obata (Ann Funct Anal 3:136–144, 2012). But, we have only been written to convey the information from quantum probability to spectral analysis of graph.     

Budget-bounded model-checking pushdown systems

We address the verification problem for concurrent programs modeled as multi-pushdown systems (MPDS). In general, MPDS are Turing powerful and hence come along with undecidability of all basic decision problems. Because of this, several subclasses of MPDS have been proposed and studied in the literature (Atig et al. in LNCS, Springer, Berlin, 2005; La Torre et al. in LICS, IEEE, 2007; Lange and Lei in Inf Didact 8, 2009; Qadeer and Rehof in TACAS, LNCS, Springer, Berlin, 2005). In this paper, we propose the class of bounded-budget MPDS, which are restricted in the sense that each stack can perform an unbounded number of context switches only if its depth is below a given bound, and a bounded number of context switches otherwise. We show that the reachability problem for this subclass is Pspace-complete and that LTL-model-checking is Exptime-complete. Furthermore, we propose a code-to-code translation that inputs a concurrent program \(P\) and produces a sequential program \(P'\) such that running \(P\) under the budget-bounded restriction yields the same set of reachable states as running \(P'\) . Moreover, detecting (fair) non-terminating executions in \(P\) can be reduced to LTL-Model-Checking of \(P'\) . By leveraging standard sequential analysis tools, we have implemented a prototype tool and applied it on a set of benchmarks, showing the feasibility of our translation.     

Frequency capping in online advertising

We study the following online problem. There are n advertisers. Each advertiser \(a_i\) has a total demand \(d_i\) and a value \(v_i\) for each supply unit. Supply units arrive one by one in an online fashion, and must be allocated to an agent immediately. Each unit is associated with a user, and each advertiser \(a_i\) is willing to accept no more than \(f_i\) units associated with any single user (the value \(f_i\) is called the frequency cap of advertiser \(a_i\) ). The goal is to design an online allocation algorithm maximizing the total value. We first show a deterministic \(3/4\) -competitiveness upper bound, which holds even when all frequency caps are \(1\) , and all advertisers share identical values and demands. A competitive ratio approaching \(1-1/e\) can be achieved via a reduction to a different model considered by Goel and Mehta (WINE ‘07: Workshop on Internet and Network, Economics: 335–340, 2007). Our main contribution is analyzing two \(3/4\) -competitive greedy algorithms for the cases of equal values, and arbitrary valuations with equal integral demand to frequency cap ratios. Finally, we give a primal-dual algorithm which may serve as a good starting point for improving upon the ratio of \(1-1/e\) .     

A note on the growth factor in Gaussian elimination for accretive-dissipative matrices

This short note proves that if \(A\) is accretive-dissipative, then the growth factor for such \(A\) in Gaussian elimination is less than \(4\) . If \(A\) is a Higham matrix, i.e., the accretive-dissipative matrix \(A\) is complex symmetric, then the growth factor is less than \(2\sqrt{2}\) . The result obtained improves those of George et al. in [Numer. Linear Algebra Appl. 9, 107–114 (2002)] and is one step closer to the final solution of Higham’s conjecture.     

An optimal boundary fair scheduling

Nowadays, many real-time operating systems discretize the time relying on a system time unit. To take this behavior into account, real-time scheduling algorithms must adopt a discrete-time model in which both timing requirements of tasks and their time allocations have to be integer multiples of the system time unit. That is, tasks cannot be executed for less than one time unit, which implies that they always have to achieve a minimum amount of work before they can be preempted. Assuming such a discrete-time model, the authors of Zhu et al. (Proceedings of the 24th IEEE international real-time systems symposium (RTSS 2003), 2003, J Parallel Distrib Comput 71(10):1411–1425, 2011) proposed an efficient “boundary fair” algorithm (named BF) and proved its optimality for the scheduling of periodic tasks while achieving full system utilization. However, BF cannot handle sporadic tasks due to their inherent irregular and unpredictable job release patterns. In this paper, we propose an optimal boundary-fair scheduling algorithm for sporadic tasks (named BF \(^2\) ), which follows the same principle as BF by making scheduling decisions only at the job arrival times and (expected) task deadlines. This new algorithm was implemented in Linux and we show through experiments conducted upon a multicore machine that BF \(^2\) outperforms the state-of-the-art discrete-time optimal scheduler (PD \(^2\) ), benefiting from much less scheduling overheads. Furthermore, it appears from these experimental results that BF \(^2\) is barely dependent on the length of the system time unit while PD \(^2\) —the only other existing solution for the scheduling of sporadic tasks in discrete-time systems—sees its number of preemptions, migrations and the time spent to take scheduling decisions increasing linearly when improving the time resolution of the system.     

Consistency properties and set based logic programming

Blair et al. (2001) developed an extension of logic programming called set based logic programming. In the theory of set based logic programming the atoms represent subsets of a fixed universe X and one is allowed to compose the one-step consequence operator with a monotonic idempotent operator O so as to ensure that the analogue of stable models in the theory are always closed under O. Marek et al. (1992, Ann Pure Appl Logic 96:231–276 1999) developed a generalization of Reiter’s normal default theories that can be applied to both default theories and logic programs which is based on an underlying consistency property. In this paper, we show how to extend the normal logic programming paradigm of Marek, Nerode, and Remmel to set based logic programming. We also show how one can obtain a new semantics for set based logic programming based on a consistency property.     

ENAMeL: A Language for Binary Correlation Matrix Memories

Despite their relative simplicity, correlation matrix memories (CMMs) are an active area of research, as they are able to be integrated into more complex architectures such as the Associative Rule Chaining Architecture (ARCA) “Austin et al. (International conference on artificial neural networks, pp 49–56, 2012)”. In this architecture, CMMs are used effectively in order to reduce the time complexity of a tree search from \(O(b^d)\) to \(O(d)\) —where \(b\) is the branching factor and \(d\) is the depth of the tree. This paper introduces the Extended Neural Associative Memory Language (ENAMeL)—a domain specific language developed to ease development of applications using CMMs. We discuss various considerations required while developing the language, and techniques used to reduce the memory requirements of CMM-based applications. Finally we show that the memory requirements of ARCA when using the ENAMeL interpreter compare favourably to our original results “Austin et al. (International conference on artificial neural networks, pp 49–56, 2012)” run in MATLAB.     

Quantum teleportation through noisy channels with multi-qubit GHZ states

We investigate two-party quantum teleportation through noisy channels for multi-qubit Greenberger–Horne–Zeilinger (GHZ) states and find which state loses less quantum information in the process. The dynamics of states is described by the master equation with the noisy channels that lead to the quantum channels to be mixed states. We analytically solve the Lindblad equation for \(n\) -qubit GHZ states \(n\in \{4,5,6\}\) where Lindblad operators correspond to the Pauli matrices and describe the decoherence of states. Using the average fidelity, we show that 3GHZ state is more robust than \(n\) GHZ state under most noisy channels. However, \(n\) GHZ state preserves same quantum information with respect to Einstein–Podolsky–Rosen and 3GHZ states where the noise is in \(x\) direction in which the fidelity remains unchanged. We explicitly show that Jung et al.’s conjecture (Phys Rev A 78:012312, 2008), namely “average fidelity with same-axis noisy channels is in general larger than average fidelity with different-axes noisy channels,” is not valid for 3GHZ and 4GHZ states.     

A Symmetric and Consistent Immersed Finite Element Method for Interface Problems

The non-conforming immersed finite element method (IFEM) developed in Li et al. (Numer Math 96:61–98, 2003) for interface problems is extensively studied in this paper. The non-conforming IFEM is very much like the standard finite element method but with modified basis functions that enforce the natural jump conditions on interface elements. While the non-conforming IFEM is simple and has reasonable accuracy, it is not fully second order accurate due to the discontinuities of the modified basis functions. While the conforming IFEM also developed in Li et al. (Numer Math 96:61–98, 2003) is fully second order accurate, the implementation is more complicated. A new symmetric and consistent IFEM has been developed in this paper. The new method maintains the advantages of the non-conforming IFEM by using the same basis functions but it is symmetric, consistent, and more important, it is second order accurate. The idea is to add some correction terms to the weak form to take into account of the discontinuities in the basis functions. Optimal error estimates are derived for the new symmetric and consistent IFE method in the \(L^2\) and \(H^1\) norms. Numerical examples presented in this paper confirm the theoretical analysis and show that the new developed IFE method has \(O(h^2)\) convergence in the \(L^\infty \) norm as well.     

Deriving length two path centered surface area for the arrangement graph: a generating function approach

We discuss the notion of \(H\) -centered surface area of a graph \(G\) , where \(H\) is a subgraph of \(G\) , i.e., the number of vertices in \(G\) at a certain distance from \(H\) , and focus on the special case when \(H\) is a length two path to derive an explicit formula for the length two path centered surface area of the general and scalable arrangement graph, following a generating function approach.     

Finding peculiar compositions of two frequent strings with background texts

We consider mining unusual patterns from a set  \(T\) of target texts. A typical method outputs unusual patterns if their observed frequencies are far from their expectation estimated under an assumed probabilistic model. However, it is difficult for the method to deal with the zero frequency and thus it suffers from data sparseness. We employ another set  \(B\) of background texts to define a composition  \(xy\) to be peculiar if both \(x\) and  \(y\) are more frequent in  \(B\) than in  \(T\) and conversely \(xy\) is more frequent in  \(T\) . \(xy\) is unusual because \(x\) and  \(y\) are infrequent in  \(T\) while \(xy\) is unexpectedly frequent compared to  \(xy\) in  \(B\) . To find frequent subpatterns and infrequent patterns simultaneously, we develop a fast algorithm using the suffix tree and show that it scales almost linearly under practical settings of parameters. Experiments using DNA sequences show that found peculiar compositions basically appear in rRNA while patterns found by an existing method seem not to relate to specific biological functions. We also show that discovered patterns have similar lengths at which the distribution of frequencies of fixed length substrings begins to skew. This fact explains why our method can find long peculiar compositions.     

Analysis and improvement of the quantum Arnold image scrambling

We investigate the quantum Arnold image scrambling proposed by Jiang et al. (Quantum Inf Process 13(5):1223–1236, 2014). It is aimed to realize Arnold and Fibonacci image scrambling in quantum computer. However, the algorithm does not perceive the particularities of “mod \(2^{n}\) ,” multiply by 2, and subtraction in binary arithmetic. In this paper, a possible simplified version is presented based on 3 theorems and a corollary which represent the particularities of binary arithmetic. The theoretical analysis indicates that the network complexity is dropped from 140n \(\sim \) 168n to 28n \(\sim \) 56n and the unitarity of circuits is not destroyed.     

An Asymptotic Preserving Method for Linear Systems of Balance Laws Based on Galerkin’s Method

We apply the concept of asymptotic preserving schemes (SIAM J Sci Comput 21:441–454, 1999) to the linearized \(p\) -system and discretize the resulting elliptic equation using standard continuous Finite Elements instead of Finite Differences. The fully discrete method is analyzed with respect to consistency, and we compare it numerically with more traditional methods such as Implicit Euler’s method.     

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”.     

Some kinds of primitive and non-primitive words

If the length of a primitive word \(p\) is equal to the length of another primitive word \(q\) , then \(p^{n}q^{m}\) is a primitive word for any \(n,m\ge 1\) and \((n,m)\ne (1,1)\) . This was obtained separately by Tetsuo Moriya in 2008 and Shyr and Yu in 1994. In this paper, we prove that if the length of \(p\) is divisible by the length of \(q\) and the length of \(p\) is less than or equal to \(m\) times the length of \(q\) , then \(p^{n}q^{m}\) is a primitive word for any \(n,m\ge 1\) and \((n,m)\ne (1,1)\) . Then we show that if \(uv,u\) are non-primitive words and the length of \(u\) is divisible by the length \(v\) or one of the length of \(u\) and \(uv\) is odd for any two nonempty words \(u\) and \(v\) , then \(u\) is a power of \(v\) .     

Query reverse engineering

In this paper, we introduce a new problem termed query reverse engineering (QRE). Given a database \(D\) and a result table \(T\) —the output of some known or unknown query \(Q\) on \(D\) —the goal of QRE is to reverse-engineer a query \(Q'\) such that the output of query \(Q'\) on database \(D\) (denoted by \(Q'(D)\) ) is equal to \(T\) (i.e., \(Q(D)\) ). The QRE problem has useful applications in database usability, data analysis, and data security. In this work, we propose a data-driven approach, TALOS for Tree-based classifier with At Least One Semantics, that is based on a novel dynamic data classification formulation and extend the approach to efficiently support the three key dimensions of the QRE problem: whether the input query is known/unknown, supporting different query fragments, and supporting multiple database versions.