Breach Remedies Including Hybrid Investments

We show that parties in bilateral trade can rely on the default common law breach remedy of ‘expectation damages’ to induce simultaneously ?rst-best relationship-speci?c investments of both the sel?sh and the cooperative kind. This can be achieved by writing a contract that speci?es a suffciently high quality level. In contrast, the result by Che and Chung (1999) that ‘reliance damages’ induce the ?rstbest in a setting of purely cooperative investments, does not generalize to the hybrid case. We also show that if the quality speci?ed in the contract is too low, ‘expectation damages’ do not necessarily induce the ex-post effcient trade decision in the presence of cooperative investments

Branching-time model checking of one-counter processes

One-counter processes (OCPs) are pushdown processes which operate only on a unary stack alphabet. We study the computational complexity of model checking computation tree logic (CTL) over OCPs. A PSPACE upper bound is inherited from the modal mu-calculus for this problem. First, we analyze the periodic behaviour of CTL over OCPs and derive a model checking algorithm whose running time is exponential only in the number of control locations and a syntactic notion of the formula that we call leftward until depth. Thus, model checking fixed OCPs against CTL formulas with a fixed leftward until depth is in P. This generalizes a result of the first author, Mayr, and To for the expression complexity of CTL's fragment EF. Second, we prove that already over some fixed OCP, CTL model checking is PSPACE-hard. Third, we show that there already exists a fixed CTL formula for which model checking of OCPs is PSPACE-hard. To obtain the latter result, we employ two results from complexity theory: (i) Converting a natural number in Chinese remainder presentation into binary presentation is in logspace-uniform NC^1 and (ii) PSPACE is AC^0-serializable. We demonstrate that our approach can be used to obtain further results. We show that model-checking CTL's fragment EF over OCPs is hard for P^NP, thus establishing a matching lower bound and answering an open question of the first author, Mayr, and To. We moreover show that the following problem is hard for PSPACE: Given a one-counter Markov decision process, a set of target states with counter value zero each, and an initial state, to decide whether the probability that the initial state will eventually reach one of the target states is arbitrarily close to 1. This improves a previously known lower bound for every level of the Boolean hierarchy by Brazdil et al

Equivalence of Deterministic One-Counter Automata is NL-complete

We prove that language equivalence of deterministic one-counter automata is NL-complete. This improves the superpolynomial time complexity upper bound shown by Valiant and Paterson in 1975. Our main contribution is to prove that two deterministic one-counter automata are inequivalent if and only if they can be distinguished by a word of length polynomial in the size of the two input automata

The Complexity of Bisimulation and Simulation on Finite Systems

In this paper the computational complexity of the (bi)simulation problem over restricted graph classes is studied. For trees given as pointer structures or terms the (bi)simulation problem is complete for logarithmic space or NC$^1$, respectively. This solves an open problem from Balc\'azar, Gabarr\'o, and S\'antha. Furthermore, if only one of the input graphs is required to be a tree, the bisimulation (simulation) problem is contained in AC$^1$ (LogCFL). In contrast, it is also shown that the simulation problem is P-complete already for graphs of bounded path-width

Breach Remedies Including Hybrid Investments

We show that parties in bilateral trade can rely on the default common law breach remedy of ‘expectation damages’ to induce simultaneously ?rst-best relationship-speci?c investments of both the sel?sh and the cooperative kind. This can be achieved by writing a contract that speci?es a suffciently high quality level. In contrast, the result by Che and Chung (1999) that ‘reliance damages’ induce the ?rstbest in a setting of purely cooperative investments, does not generalize to the hybrid case. We also show that if the quality speci?ed in the contract is too low, ‘expectation damages’ do not necessarily induce the ex-post effcient trade decision in the presence of cooperative investments.breach remedies; incomplete contracts; hybrid investments; cooperative investments; sel?sh investments