Automatic Generation of Invariants for Circular Derivations in {SUP(LA)} 1

The hierarchic combination of linear arithmetic and firstorder logic with free function symbols, FOL(LA), results in a strictly more expressive logic than its two parts. The SUP(LA) calculus can be turned into a decision procedure for interesting fragments of FOL(LA). For example, reachability problems for timed automata can be decided by SUP(LA) using an appropriate translation into FOL(LA). In this paper, we extend the SUP(LA) calculus with an additional inference rule, automatically generating inductive invariants from partial SUP(LA) derivations. The rule enables decidability of more expressive fragments, including reachability for timed automata with unbounded integer variables. We have implemented the rule in the SPASS(LA) theorem prover with promising results, showing that it can considerably speed up proof search and enable termination of saturation for practically relevant problems

A theory of normed simulations

In existing simulation proof techniques, a single step in a lower-level specification may be simulated by an extended execution fragment in a higher-level one. As a result, it is cumbersome to mechanize these techniques using general purpose theorem provers. Moreover, it is undecidable whether a given relation is a simulation, even if tautology checking is decidable for the underlying specification logic. This paper introduces various types of normed simulations. In a normed simulation, each step in a lower-level specification can be simulated by at most one step in the higher-level one, for any related pair of states. In earlier work we demonstrated that normed simulations are quite useful as a vehicle for the formalization of refinement proofs via theorem provers. Here we show that normed simulations also have pleasant theoretical properties: (1) under some reasonable assumptions, it is decidable whether a given relation is a normed forward simulation, provided tautology checking is decidable for the underlying logic; (2) at the semantic level, normed forward and backward simulations together form a complete proof method for establishing behavior inclusion, provided that the higher-level specification has finite invisible nondeterminism.Comment: 31 pages, 10figure

Model Checking CTL is Almost Always Inherently Sequential

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations---restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that, in cases where the combined complexity is of relevance, approaching CTL model checking by parallelism cannot be expected to result in any significant speedup. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL+, and ECTL+

Extended Computation Tree Logic

We introduce a generic extension of the popular branching-time logic CTL which refines the temporal until and release operators with formal languages. For instance, a language may determine the moments along a path that an until property may be fulfilled. We consider several classes of languages leading to logics with different expressive power and complexity, whose importance is motivated by their use in model checking, synthesis, abstract interpretation, etc. We show that even with context-free languages on the until operator the logic still allows for polynomial time model-checking despite the significant increase in expressive power. This makes the logic a promising candidate for applications in verification. In addition, we analyse the complexity of satisfiability and compare the expressive power of these logics to CTL* and extensions of PDL

Symmetry in temporal logic model checking

Temporal logic model checking involves checking the state-space of a model of a system to determine whether errors can occur in the system. Often this involves checking symmetrically equivalent areas of the state-space. The use of symmetry reduction to increase the efficiency of model checking has inspired a wealth of activity in the area of model checking research. We provide a survey of the associated literature

A Complete Axiom System for Propositional Interval Temporal Logic with Infinite Time

Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We solve the longstanding open problem of finding a complete axiom system for basic quantifier-free propositional ITL (PITL) with infinite time for analysing nonterminating computational systems. Our completeness proof uses a reduction to completeness for PITL with finite time and conventional propositional linear-time temporal logic. Unlike completeness proofs of equally expressive logics with nonelementary computational complexity, our semantic approach does not use tableaux, subformula closures or explicit deductions involving encodings of omega automata and nontrivial techniques for complementing them. We believe that our result also provides evidence of the naturalness of interval-based reasoning

A multilevel intervention to increase physical activity and improve healthy eating and physical literacy among young children (ages 3-5) attending early childcare centres: the Healthy Start-Départ Santé cluster randomised controlled trial study protocol

Abstract: Background: Childhood obesity is a growing concern for public health. Given a majority of children in many countries spend approximately 30 h per week in early childcare centers, this environment represents a promising setting for implementing strategies to foster healthy behaviours for preventing and controlling childhood obesity. Healthy Start-Départ Santé was designed to promote physical activity, physical literacy, and healthy eating among preschoolers. The objectives of this study are to assess the effectiveness of the Healthy Start-Départ Santé intervention in improving physical activity levels, physical literacy, and healthy eating among preschoolers attending early childcare centers. Methods/Design: This study follows a cluster randomized controlled trial design in which the childcare centers are randomly assigned to receive the intervention or serve as usual care controls. The Healthy Start-Départ Santé intervention is comprised of interlinked components aiming to enable families and educators to integrate physical activity and healthy eating in the daily lives of young children by influencing factors at the intrapersonal, interpersonal, organizational, community, physical environment and policy levels. The intervention period, spanning 6-8 months, is preceded and followed by data collections. Participants are recruited from 61 childcare centers in two Canadian provinces, New Brunswick and Saskatchewan. Centers eligible for this study have to prepare and provide meals for lunch and have at least 20 children between the ages of 3 and 5. Centers are excluded if they have previously received a physical activity or nutrition promoting intervention. Eligible centers are stratified by province, geographical location (urban or rural) and language (English or French), then recruited and randomized using a one to one protocol for each stratum. Data collection is ongoing. The primary study outcomes are assessed using accelerometers (physical activity levels), the Test of Gross Motor Development-II (physical literacy), and digital photography-assisted weighted plate waste (food intake). Discussion: The multifaceted approach of Healthy Start-Départ Santé positions it well to improve the physical literacy and both dietary and physical activity behaviors of children attending early childcare centers. The results of this study will be of relevance given the overwhelming prevalence of overweight and obesity in children worldwide. Trial registration: NCT02375490 (ClinicalTrials.gov registry)