Model Checking the Quantitative mu-Calculus on Linear Hybrid Systems

We study the model-checking problem for a quantitative extension of the modal mu-calculus on a class of hybrid systems. Qualitative model checking has been proved decidable and implemented for several classes of systems, but this is not the case for quantitative questions that arise naturally in this context. Recently, quantitative formalisms that subsume classical temporal logics and allow the measurement of interesting quantitative phenomena were introduced. We show how a powerful quantitative logic, the quantitative mu-calculus, can be model checked with arbitrary precision on initialised linear hybrid systems. To this end, we develop new techniques for the discretisation of continuous state spaces based on a special class of strategies in model-checking games and present a reduction to a class of counter parity games.Comment: LMCS submissio

Model Checking Synchronized Products of Infinite Transition Systems

Formal verification using the model checking paradigm has to deal with two aspects: The system models are structured, often as products of components, and the specification logic has to be expressive enough to allow the formalization of reachability properties. The present paper is a study on what can be achieved for infinite transition systems under these premises. As models we consider products of infinite transition systems with different synchronization constraints. We introduce finitely synchronized transition systems, i.e. product systems which contain only finitely many (parameterized) synchronized transitions, and show that the decidability of FO(R), first-order logic extended by reachability predicates, of the product system can be reduced to the decidability of FO(R) of the components. This result is optimal in the following sense: (1) If we allow semifinite synchronization, i.e. just in one component infinitely many transitions are synchronized, the FO(R)-theory of the product system is in general undecidable. (2) We cannot extend the expressive power of the logic under consideration. Already a weak extension of first-order logic with transitive closure, where we restrict the transitive closure operators to arity one and nesting depth two, is undecidable for an asynchronous (and hence finitely synchronized) product, namely for the infinite grid.Comment: 18 page

The Complexity of Model Checking Higher-Order Fixpoint Logic

Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of programs that are not expressible in the modal \lambda-calculus. This paper provides complexity results for its model checking problem. In particular we consider those fragments of HFL built by using only types of bounded order k and arity m. We establish k-fold exponential time completeness for model checking each such fragment. For the upper bound we use fixpoint elimination to obtain reachability games that are singly-exponential in the size of the formula and k-fold exponential in the size of the underlying transition system. These games can be solved in deterministic linear time. As a simple consequence, we obtain an exponential time upper bound on the expression complexity of each such fragment. The lower bound is established by a reduction from the word problem for alternating (k-1)-fold exponential space bounded Turing Machines. Since there are fixed machines of that type whose word problems are already hard with respect to k-fold exponential time, we obtain, as a corollary, k-fold exponential time completeness for the data complexity of our fragments of HFL, provided m exceeds 3. This also yields a hierarchy result in expressive power.Comment: 33 pages, 2 figures, to be published in Logical Methods in Computer Scienc

Dense-Timed Petri Nets: Checking Zenoness, Token liveness and Boundedness

We consider Dense-Timed Petri Nets (TPN), an extension of Petri nets in which each token is equipped with a real-valued clock and where the semantics is lazy (i.e., enabled transitions need not fire; time can pass and disable transitions). We consider the following verification problems for TPNs. (i) Zenoness: whether there exists a zeno-computation from a given marking, i.e., an infinite computation which takes only a finite amount of time. We show decidability of zenoness for TPNs, thus solving an open problem from [Escrig et al.]. Furthermore, the related question if there exist arbitrarily fast computations from a given marking is also decidable. On the other hand, universal zenoness, i.e., the question if all infinite computations from a given marking are zeno, is undecidable. (ii) Token liveness: whether a token is alive in a marking, i.e., whether there is a computation from the marking which eventually consumes the token. We show decidability of the problem by reducing it to the coverability problem, which is decidable for TPNs. (iii) Boundedness: whether the size of the reachable markings is bounded. We consider two versions of the problem; namely semantic boundedness where only live tokens are taken into consideration in the markings, and syntactic boundedness where also dead tokens are considered. We show undecidability of semantic boundedness, while we prove that syntactic boundedness is decidable through an extension of the Karp-Miller algorithm.Comment: 61 pages, 18 figure

Decidability of higher-order matching

We show that the higher-order matching problem is decidable using a game-theoretic argument.Comment: appears in LMCS (Logical Methods in Computer Science

The impact of hydrothermal carbonisation on the char reactivity of biomass

Hydrothermal carbonisation (HTC) is an attractive biomass pre-treatment as it produces a coal-like fuel, can easily process wet biomass and wastes, and lowers the risk of slagging and fouling in pulverised fuel (PF) combustion boilers. One of the major factors in determining the suitability of a fuel as a coal replacement for PF combustion is matching the char reactivity and volatile matter content to that of coals, as these significantly affect heat release and flame stability. The char reactivity of wood and olive cake biocoals and their respective drop tube furnace chars have been studied using thermogravimetric analysis in comparison to other biomass fuels and high-volatile bituminous coal. It was found that HTC reduces the reactivity of biomass, and in the case of HTC of wood pellets the resulting biocoal has a char reactivity similar to that of high-volatile bituminous coal. Proximate analysis, X-ray fluorescence analysis, and textural characterisation were used to show that this effect is caused primarily by removal of catalytic alkali and alkaline earth metals. Subsequent torrefaction of the wood biocoals was performed to tailor their volatile matter content to match that of sub-bituminous and high volatile bituminous coals without major impact on char reactivity

Beyond Language Equivalence on Visibly Pushdown Automata

We study (bi)simulation-like preorder/equivalence checking on the class of visibly pushdown automata and its natural subclasses visibly BPA (Basic Process Algebra) and visibly one-counter automata. We describe generic methods for proving complexity upper and lower bounds for a number of studied preorders and equivalences like simulation, completed simulation, ready simulation, 2-nested simulation preorders/equivalences and bisimulation equivalence. Our main results are that all the mentioned equivalences and preorders are EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for visibly one-counter automata improves also the previously known DP-hardness results for ordinary one-counter automata and one-counter nets. Finally, we study regularity checking problems for visibly pushdown automata and show that they can be decided in polynomial time.Comment: Final version of paper, accepted by LMC

KAJI AWAL TURBIN AIR DARRIEUS 3 BLADE HYDROFOIL NACA 0018 PADA VARIASI BILANGAN REYNOLD

Kebutuhan akan energi dari tahun ke tahun semakin meningkat sementara cadangan energi yang berasal dari fossil seperti minyak bumi dan batu bara semakin menipis. Hal ini akan menyebabkan terjadinya krisis energi karena sumber energi tersebut adalah sumber energi yang tak terbarukan. Untuk mengatasi permasalahan energi ini perlu dicari sumber-sumber energi baru yang terbarukan, sehingga tidak akan terjadi krisis energi di masa yang akan datang. Indonesia memiliki lautan yang sangat luas, sehingga potensi arus lautnya dapat dimanfaatkan sebagai energi alternatif. Penelitian ini adalah melakukan pengujian terhadap turbin Darrieus. Turbin ini memiliki diameter 20 cm dan tinggi 20 cm, blade yang digunakan adalah hydrofoil NACA 0018 dengan panjang chord 6,5 cm. Pengujian dilakukan pada sebuah saluran uji yang memiliki penampang persegi panjang 30 x 32 cm dengan variasi bilangan Reynold 6370, 11980 dan 17615 untuk mencari daya dan efisiensi yang dihasilkan turbin tersebut. Dari hasil pengujian, daya yang dihasilkan turbin Darrieus tersebut pada bilangan Reynold 6370, 11980 dan 17615 berturut-turut adalah 0,00339 Watt, 0,009 Watt dan 0,018 Watt sedangkan efisiensinya 21,95 %, 7,37 % dan 4,52 %. Kata kunci: Turbin Darrieus, NACA 0018, bilangan Reynold dan efisiens

Sparse Positional Strategies for Safety Games

We consider the problem of obtaining sparse positional strategies for safety games. Such games are a commonly used model in many formal methods, as they make the interaction of a system with its environment explicit. Often, a winning strategy for one of the players is used as a certificate or as an artefact for further processing in the application. Small such certificates, i.e., strategies that can be written down very compactly, are typically preferred. For safety games, we only need to consider positional strategies. These map game positions of a player onto a move that is to be taken by the player whenever the play enters that position. For representing positional strategies compactly, a common goal is to minimize the number of positions for which a winning player's move needs to be defined such that the game is still won by the same player, without visiting a position with an undefined next move. We call winning strategies in which the next move is defined for few of the player's positions sparse. Unfortunately, even roughly approximating the density of the sparsest strategy for a safety game has been shown to be NP-hard. Thus, to obtain sparse strategies in practice, one either has to apply some heuristics, or use some exhaustive search technique, like ILP (integer linear programming) solving. In this paper, we perform a comparative study of currently available methods to obtain sparse winning strategies for the safety player in safety games. We consider techniques from common knowledge, such as using ILP or SAT (satisfiability) solving, and a novel technique based on iterative linear programming. The results of this paper tell us if current techniques are already scalable enough for practical use.Comment: In Proceedings SYNT 2012, arXiv:1207.055