We show that Cubicle, an SMT-based infinite-state model checker, can be applied as a verification engine for GLog, a logic-based language based on relational updates rules that has been applied to specify topology-sensitive distributed protocols with asynchronous communication. In this setting, the absence of protocol anomalies can be reduced to a coverability problem in which the initial set of configurations is not fixed a priori (Existential Coverability Problem). Existential Coverability in GLog can naturally be expressed into Parameterized Verification judgements in Cubicle. The encoding is based on a translation of relational update rules into transition rules that modify cells of unbounded arrays. To show the effectiveness of the approach, we discuss several verification problems for distributed protocols and distributed objects, a challenging task for traditional verification tools. The experimental results show the flexibility and robustness of Cubicle for the considered class of protocol examples.

In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice Mk (the unique lattice with k + 2 elements and one anti-chain of length k) and find the maximal k for which it is isomorphic to a subgraph of the reduction graph of a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such k is 2 and there are cases where there is no maximum. No other intermediate option is possible.

The general position number gp( G) of a graph G is the cardinality of a largest set of vertices S such that no element of S lies on a geodesic between two other elements of S. The complementary prism G[Formula: see text] of G is the graph formed from the disjoint union of G and its complement [Formula: see text] by adding the edges of a perfect matching between them. It is proved that gp( G[Formula: see text]) ≤ n( G) + 1 if G is connected and gp( G[Formula: see text]) ≤ n( G) if G is disconnected. Graphs G for which gp( G[Formula: see text]) = n( G) + 1 holds, provided that both G and [Formula: see text] are connected, are characterized. A sharp lower bound on gp( G[Formula: see text]) is proved. If G is a connected bipartite graph or a split graph then gp( G[Formula: see text]) ∈ { n( G), n( G)+1}. Connected bipartite graphs and block graphs for which gp( G[Formula: see text]) = n( G) + 1 holds are characterized. A family of block graphs is constructed in which the gp-number of their complementary prisms is arbitrary smaller than their order.

Many partial order methods use some special condition for ensuring that the analysis is not terminated prematurely. In the case of stubborn set methods for safety properties, implementation of the condition is usually based on recognizing the terminal strong components of the reduced state space and, if necessary, expanding the stubborn sets used in their roots. In an earlier study it was pointed out that if the system may execute a cycle consisting of only invisible actions and that cycle is concurrent with the rest of the system in a non-obvious way, then the method may be fooled to construct all states of the full parallel composition. This problem is solved in this study by a method that “freezes” the actions in the cycle. The new method also preserves fair testing equivalence, making it usable for the verification of many progress properties.

Abductive Logic Programming (ALP) has been proven very effective for formalizing societies of agents, commitments and norms, in particular by mapping the most common deontic operators (obligation, prohibition, permission) to abductive expectations. In our previous works, we have shown that ALP is a suitable framework for representing norms. Normative reasoning and query answering were accommodated by the same abductive proof procedure, named 𝒮CIFF. In this work, we introduce a defeasible flavour in this framework, in order to possibly discharge obligations in some scenarios. Abductive expectations can also be qualified as dischargeable, in the new, extended syntax. Both declarative and operational semantics are improved accordingly, and proof of soundness is given under syntax allowedness conditions Moreover, the dischargement itself might be proved invalid, or incoherent with the rules, due to new knowledge provided later on. In such a case, a discharged expectation might be reinstated and hold again after some evidence is given. We extend the notion of dischargement to take into consideration also the reinstatement of expectations. The expressiveness and power of the extended framework, named 𝒮CIFF𝒟, is shown by modeling and reasoning upon a fragment of the Japanese Civil Code. In particular, we consider a case study concerning manifestations of intention and their rescission (Section II of the Japanese Civil Code).

Parkinson’s disease (PD) is the second after Alzheimer’s most popular neurodegenerative disease (ND). Cures for both NDs are currently unavailable. OBJECTIVE: The purpose of our study was to predict the results of different PD patients’ treatments in order to find an optimal one. METHODS: We have compared rough sets (RS) and others, in short, machine learning (ML) models to describe and predict disease progression expressed as UPDRS values (Unified Parkinson’s Disease Rating Scale) in three groups of Parkinson’s patients: 23 BMT (Best Medical Treatment) patients on medication; 24 DBS patients on medication and on DBS therapy (Deep Brain Stimulation) after surgery performed during our study; and 15 POP (Postoperative) patients who had had surgery earlier (before the beginning of our research). Every PD patient had three visits approximately every six months. The first visit for DBS patients was before surgery. On the basis of the following condition attributes: disease duration, saccadic eye movement parameters, and neuropsychological tests: PDQ39 (Parkinson’s Disease Questionnaire - disease-specific health-related quality-of-life questionnaire), and Epworth Sleepiness Scale tests we have estimated UPDRS changes (as the decision attribute). RESULTS: By means of RS rules obtained for the first visit of BMT/DBS/POP patients, we have predicted UPDRS values in the following year (two visits) with global accuracy of 70% for both BMT visits; 56% for DBS, and 67%, 79% for POP second and third visits. The accuracy obtained by ML models was generally in the same range, but it was calculated separately for different sessions (MedOFF/MedON). We have used RS rules obtained in BMT patients to predict UPDRS of DBS patients; for the first session DBSW1: global accuracy was 64%, for the second DBSW2: 85% and the third DBSW3: 74% but only for DBS patients during stimulation-ON. ML models gave better accuracy for DBSW1/W2 session S1(MedOFF): 88%, but inferior results for session S3 (MedON): 58% and 54%. Both RS and ML could not predict UPDRS in DBS patients during stimulation-OFF visits because of differences in UPDRS. By using RS rules from BMT or DBS patients we could not predict UPDRS of POP group, but with certain limitations (only for MedON), we derived such predictions for the POP group from results of DBS patients by using ML models (60%). SIGNIFICANCE: Thanks to our RS and ML methods, we were able to predict Parkinson’s disease (PD) progression in dissimilar groups of patients with different treatments. It might lead, in the future, to the discovery of universal rules of PD progression and optimise the treatment.

For a network, edge/node-independent spanning trees (ISTs) can not only tolerate faulty edges/nodes, but also be used to distribute secure messages. As important node-symmetric variants of the hypercubes, the augmented cubes have received much attention from researchers. The n-dimensional augmented cube AQn is both (2n ‒ 1)-edge-connected and (2n ‒ 1)-nodeconnected (n ≢ 3), thus the well-known edge conjecture and node conjecture of ISTs are both interesting questions in AQn. So far, the edge conjecture on augmented cubes was proved to be true. However, the node conjecture on AQn is still open. In this paper, we further study the construction principle of the node-ISTs by using the double neighbors of every node in the higher dimension. We prove the existence of 2k − 1 node-ISTs rooted at node 0 in A Q n ( 00...0 ︸ n−k )(n≥k≥4) by proposing an ingenious way of construction and propose a corresponding O(NlogN) time algorithm, where N = 2k is the number of nodes in A Q n ( 00...0 ︸ n−k ) .

We consider the problem of obtaining parameterized lower bounds for the size of arithmetic circuits computing polynomials with the degree of the polynomial as the parameter. We consider the following special classes of multilinear algebraic branching programs: 1) Read Once Oblivious Branching Programs (ROABPs), 2) Strict interval branching programs, 3) Sum of read once formulas with restricted ordering. We obtain parameterized lower bounds (i.e., nΩ( t( k)) lower bound for some function t of k) on the size of the above models computing a multilinear polynomial that can be computed by a depth four circuit of size g( k) n O(1) for some computable function g. Further, we obtain a parameterized separation between ROABPs and read-2 ABPs. This is obtained by constructing a degree k polynomial that can be computed by a read-2 ABP of small size such that the rank of the partial derivative matrix under any partition of the variables is large.

Finite topological spaces and their dimensions have many applications in computer science, e.g., in digital topology, computer graphics and the analysis and synthesis of digital images. Georgiou et. al. [11] provided a polynomial algorithm for computing the covering dimension dim( X; 𝒯) of a finite topological space (X; 𝒯). In addition, they asked whether algorithms of the same complexity for computing the small inductive dimension ind( X; 𝒯) and the large inductive dimension Ind( X; 𝒯) can be developed. The first problem was solved in a previous paper [4]. Using results of the that paper, we also solve the second problem in this paper. We present a polynomial algorithm for Ind( X; 𝒯), so that there are now efficient algorithms for the three most important notions of a dimension in topology. Our solution reduces the computation of Ind( X; 𝒯), where the specialisation pre-order of ( X; 𝒯) is taken as input, to the computation of the maximal height of a specific class of directed binary trees within the partially ordered set. For the latter an efficient algorithm is presented that is based on order- and graph-theoretic ideas. Also refinements and variants of the algorithm are discussed.

We construct a first-order formula φ such that all finite models of φ are non-narrow rectangular grids without using any binary relations other than the grid neighborship relations. As a corollary, we prove that a set A ⊆ ℕ is a spectrum of a formula which has only planar models if numbers n ∈ A can be recognized by a non-deterministic Turing machine (or a one-dimensional cellular automaton) in time t(n) and space s(n), where t(n)s(n) ≤ n and t(n); s(n) = Ω(log(n)).