Weak Singular Hybrid Automata

The framework of Hybrid automata, introduced by Alur, Courcourbetis, Henzinger, and Ho, provides a formal modeling and analysis environment to analyze the interaction between the discrete and the continuous parts of cyber-physical systems. Hybrid automata can be considered as generalizations of finite state automata augmented with a finite set of real-valued variables whose dynamics in each state is governed by a system of ordinary differential equations. Moreover, the discrete transitions of hybrid automata are guarded by constraints over the values of these real-valued variables, and enable discontinuous jumps in the evolution of these variables. Singular hybrid automata are a subclass of hybrid automata where dynamics is specified by state-dependent constant vectors. Henzinger, Kopke, Puri, and Varaiya showed that for even very restricted subclasses of singular hybrid automata, the fundamental verification questions, like reachability and schedulability, are undecidable. In this paper we present \emph{weak singular hybrid automata} (WSHA), a previously unexplored subclass of singular hybrid automata, and show the decidability (and the exact complexity) of various verification questions for this class including reachability (NP-Complete) and LTL model-checking (PSPACE-Complete). We further show that extending WSHA with a single unrestricted clock or extending WSHA with unrestricted variable updates lead to undecidability of reachability problem

Merging fragments of classical logic

We investigate the possibility of extending the non-functionally complete logic of a collection of Boolean connectives by the addition of further Boolean connectives that make the resulting set of connectives functionally complete. More precisely, we will be interested in checking whether an axiomatization for Classical Propositional Logic may be produced by merging Hilbert-style calculi for two disjoint incomplete fragments of it. We will prove that the answer to that problem is a negative one, unless one of the components includes only top-like connectives.Comment: submitted to FroCoS 201

Carvedilol Ameliorates Potassium Dichromate-Induced Acute Renal Injury in Rats: Plausible Role of Inflammation and Apoptosis

Environmental and occupational exposure to hexavalent chromium [Cr(VI)] via textile manufacture, metallurgy, spray paints, stainless steel industries, drinking water containing chromium are often known to cause acute renal injury in humans and animals. Nephrotoxicity is the major effect of chromium poisoning. In the present study, we investigated the potential renoprotective effect and underlying mechanisms of carvedilol using rat model of potassium dichromate (K2Cr2O7)-induced nephrotoxicity. Exploration of the underlying mechanisms of carvedilol revealed that carvedilol attenuated nuclear translocation and DNA binding activity of NF-κB (p65), restored antioxidant and mitochondrial respiratory enzyme activities and attenuated apoptosis related protein expressions in kidney tissues. The serum levels of TNF-α, the renal iNOS and myeloperoxidase activity were significantly decreased in carvedilol pre-treated K2Cr2O7-induced nephrotoxic rats. These results were further supported and confirmed by histological findings. In conclusion, the findings of the present study demonstrated that carvedilol is an effective chemoprotectant against K2Cr2O7-induced nephrotoxicity in rats

Interrupt Timed Automata: verification and expressiveness

We introduce the class of Interrupt Timed Automata (ITA), a subclass of hybrid automata well suited to the description of timed multi-task systems with interruptions in a single processor environment. While the reachability problem is undecidable for hybrid automata we show that it is decidable for ITA. More precisely we prove that the untimed language of an ITA is regular, by building a finite automaton as a generalized class graph. We then establish that the reachability problem for ITA is in NEXPTIME and in PTIME when the number of clocks is fixed. To prove the first result, we define a subclass ITA- of ITA, and show that (1) any ITA can be reduced to a language-equivalent automaton in ITA- and (2) the reachability problem in this subclass is in NEXPTIME (without any class graph). In the next step, we investigate the verification of real time properties over ITA. We prove that model checking SCL, a fragment of a timed linear time logic, is undecidable. On the other hand, we give model checking procedures for two fragments of timed branching time logic. We also compare the expressive power of classical timed automata and ITA and prove that the corresponding families of accepted languages are incomparable. The result also holds for languages accepted by controlled real-time automata (CRTA), that extend timed automata. We finally combine ITA with CRTA, in a model which encompasses both classes and show that the reachability problem is still decidable. Additionally we show that the languages of ITA are neither closed under complementation nor under intersection

Complexity and Expressivity of Branching- and Alternating-Time Temporal Logics with Finitely Many Variables

We show that Branching-time temporal logics CTL and CTL*, as well as Alternating-time temporal logics ATL and ATL*, are as semantically expressive in the language with a single propositional variable as they are in the full language, i.e., with an unlimited supply of propositional variables. It follows that satisfiability for CTL, as well as for ATL, with a single variable is EXPTIME-complete, while satisfiability for CTL*, as well as for ATL*, with a single variable is 2EXPTIME-complete,--i.e., for these logics, the satisfiability for formulas with only one variable is as hard as satisfiability for arbitrary formulas.Comment: Prefinal version of the published pape

Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking

One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively large BDD for the orbit relation. Dynamic symmetry reduction calculates representatives of equivalence classes of states dynamically and thus avoids the construction of the orbit relation. In this paper, we present a new efficient model checking algorithm based on dynamic symmetry reduction. Our experiments show that the algorithm is very fast and allows the verification of larger systems. We additionally implemented the use of state symmetries for symbolic symmetry reduction. To our knowledge we are the first who investigated state symmetries in combination with BDD based symbolic model checking

A SAT-Based Encoding of the One-Pass and Tree-Shaped Tableau System for LTL

A new one-pass and tree-shaped tableau system for LTL sat- isfiability checking has been recently proposed, where each branch can be explored independently from others and, furthermore, directly cor- responds to a potential model of the formula. Despite its simplicity, it proved itself to be effective in practice. In this paper, we provide a SAT-based encoding of such a tableau system, based on the technique of bounded satisfiability checking. Starting with a single-node tableau, i.e., depth k of the tree-shaped tableau equal to zero, we proceed in an incremental fashion. At each iteration, the tableau rules are encoded in a Boolean formula, representing all branches of the tableau up to the current depth k. A typical downside of such bounded techniques is the effort needed to understand when to stop incrementing the bound, to guarantee the completeness of the procedure. In contrast, termination and completeness of the proposed algorithm is guaranteed without com- puting any upper bound to the length of candidate models, thanks to the Boolean encoding of the PRUNE rule of the original tableau system. We conclude the paper by describing a tool that implements our procedure, and comparing its performance with other state-of-the-art LTL solvers

Vectorial Languages and Linear Temporal Logic

International audienceDetermining for a given deterministic complete automaton the sequence of visited states while reading a given word is the core of important problems with automata-based solutions, such as approximate string matching. The main difficulty is to do this computation efficiently, especially when dealing with very large texts. Considering words as vectors and working on them using vectorial (parallel) operations allows to solve the problem faster than in linear time using sequential computations. In this paper, we show first that the set of vectorial operations needed by an algorithm representing a given automaton depends only on the language accepted by the automaton. We give precise characterizations of vectorial algorithms for star-free, solvable and regular languages in terms of the vectorial operations allowed. We also consider classes of languages associated with restricted sets of vectorial operations and relate them with languages defined by fragments of linear temporal logic. Finally, we consider the converse problem of constructing an automaton from a given vectorial algorithm. As a byproduct, we show that the satisfiability problem for some extensions of linear-time temporal logic characterizing solvable and regular languages is PSPACE-complete

Satisfiability Checking for Mission-Time LTL

Mission-time LTL (MLTL) is a bounded variant of MTL over naturals designed to generically specify requirements for mission-based system operation common to aircraft, spacecraft, vehicles, and robots. Despite the utility of MLTL as a specification logic, major gaps remain in analyzing MLTL, e.g., for specification debugging or model checking, centering on the absence of any complete MLTL satisfiability checker. We prove that the MLTL satisfiability checking problem is NEXPTIME-complete and that satisfiability checking MLTL0 , the variant of MLTL where all intervals start at 0, is PSPACE-complete. We introduce translations for MLTL-to-LTL, MLTL-to-LTLf , MLTL-to-SMV, and MLTL-to-SMT, creating four options for MLTL satisfiability checking. Our extensive experimental evaluation shows that the MLTL-to-SMT transition with the Z3 SMT solver offers the most scalable performance