Specification of Synchronous Network Flooding in Temporal Logic

In distributed network algorithms, network flooding algorithm is considered one of the simplest and most fundamental algorithms. This research specifies the basic synchronous memory-less network flooding algorithm where nodes on the network don’t have memory, for any fixed size of network, in Linear Temporal Logic. The specification can be customized to any single network topology or class of topologies. A specification of the termination problem is formulated and used to compare different topologies for earlier termination. This research gives a worked example of one topology resulting in earlier termination than another, for which we perform a formal verification using the model checker NuSMV

What is decidable under the TSO memory model?

We consider the verification problem of safety and liveness properties of finite-state programs running under the Total Store Ordering (TSO) memory model.We first review the decidability/complexity results regarding these two problems and then show that the termination problem is decidable.

All-Instances Oblivious Chase Termination is Undecidable for Single-Head Binary TGDs

The chase is a famous algorithmic procedure in database theory with numerous applications in ontology-mediated query answering. We consider static analysis of the chase termination problem, which asks, given set of TGDs, whether the chase terminates on all input databases. The problem was recently shown to be undecidable by Gogacz et al. for sets of rules containing only ternary predicates. In this work, we show that undecidability occurs already for sets of single-head TGD over binary vocabularies. This question is relevant since many real-world ontologies, e.g., those from the Horn fragment of the popular OWL, are of this shape.

Polynomial Loops: Beyond Termination

In the last years, several works were concerned with identifying classes of programswhere termination is decidable. We consider triangular weakly non-linear loops(twn-loops) over a ring Z ≤ S ≤ R_A , where R_A is the set of all real algebraicnumbers. Essentially, the body of such a loop is a single assignment(x_1, ..., x_d) ← (c_1 · x_1 + pol_1, ..., c_d · x_d + pol_d)where each x_i is a variable, c_i ∈ S, and each pol_i is a (possibly non-linear)polynomial over S and the variables x_{i+1}, ..., x_d. Recently, we showed thattermination of such loops is decidable for S = R_A and non-termination issemi-decidable for S = Z and S = Q.In this paper, we show that the halting problem is decidable for twn-loops over anyring Z ≤ S ≤ R_A. In contrast to the termination problem, where termination on allinputs is considered, the halting problem is concerned with termination on a giveninput. This allows us to compute witnesses for non-termination.Moreover, we present the first computability results on the runtime complexity ofsuch loops. More precisely, we show that for twn-loops over Z one can alwayscompute a polynomial f such that the length of all terminating runs is boundedby f( || (x_1, ..., x_d) || ), where || · || denotes the 1-norm. As a corollary, weobtain that the runtime of a terminating triangular linear loop over Z isat most linear.

Query Answering with Guarded Existential Rules under Stable Model Semantics

In this paper, we study the problem of query answering with guarded existential rules (also called GNTGDs) under stable model semantics. Our goal is to use existing answer set programming (ASP) solvers. However, ASP solvers handle only finitely-ground logic programs while the program translated from GNTGDs by Skolemization is not in general. To address this challenge, we introduce two novel notions of (1) guarded instantiation forest to describe the instantiation of GNTGDs and (2) prime block to characterize the repeated infinitely-ground program translated from GNTGDs. Using these notions, we prove that the ground termination problem for GNTGDs is decidable. We also devise an algorithm for query answering with GNTGDs using ASP solvers. We have implemented our approach in a prototype system. The evaluation over a set of benchmarks shows encouraging results.