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The evolution of strong reproductive isolation
Get PDFFelsenstein distinguished two ways by which selection can directly strengthen isolation. First, a modifier that strengthens prezygotic isolation can be favored everywhere. This fits with the traditional view of reinforcement as an adaptation to reduce deleterious hybridization by strengthening assortative mating. Second, selection can favor association between different incompatibilities, despite recombination. We generalize this "two allele" model to follow associations among any number of incompatibilities, which may include both assortment and hybrid inviability. Our key argument is that this process, of coupling between incompatibilities, may be quite different from the usual view of reinforcement: strong isolation can evolve through the coupling of any kind of incompatibility, whether prezygotic or postzygotic. Single locus incompatibilities become coupled because associations between them increase the variance in compatibility, which in turn increases mean fitness if there is positive epistasis. Multiple incompatibilities, each maintained by epistasis, can become coupled in the same way. In contrast, a single-locus incompatibility can become coupled with loci that reduce the viability of haploid hybrids because this reduces harmful recombination. We obtain simple approximations for the limits of tight linkage, and strong assortment, and show how assortment alleles can invade through associations with other components of reproductive isolation
Distributed, modular Htl
Get PDFThe Hierarchical Timing Language (HTL) is a real-time coordination language for distributed control systems. HTL programs must be checked for well-formedness, race freedom, transmission safety (schedulability of inter-host communication), and time safety (schedulability of host computation). We present a modular abstract syntax and semantics for HTL, modular checks of well-formedness, race freedom, and transmission safety, and modular code distribution. Our contributions here complement previous results on HTL time safety and modular code generation. Modularity in HTL can be utilized in easy program composition as well as fast program analysis and code generation, but also in so-called runtime patching, where program components may be modified at runtime
Finitary winning in omega-regular games
Get PDFGames on graphs with omega-regular objectives provide a model for the control and synthesis of reactive systems. Every omega-regular objective can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens “eventually“ Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds). However, the classical liveness formulation suffers from the drawback that the time until something good happens may be unbounded. A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity. Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions. While for one-shot liveness (reachability) objectives, classical and finitary liveness coincide, for repeated liveness (Buchi) objectives, the finitary formulation is strictly stronger. In this work we study games with finitary parity and Streett objectives. We prove the determinacy of these games, present algorithms for solving these games, and characterize the memory requirements of winning strategies. We show that finitary parity games can be solved in polynomial time, which is not known for infinitary parity games. For finitary Streett games, we give an EXPTIME algorithm and show that the problem is NP-hard. Our algorithms can be used, for example, for synthesizing controllers that do not let the response time of a system increase without bound
Synthesizing robust systems
Get PDFMany specifications include assumptions on the environment. If the environment satisfies the assumptions then a correct system reacts as intended. However, when the environment deviates from its expected behavior, a correct system can behave arbitrarily. We want to synthesize robust systems that degrade gracefully, i.e., a small number of environment failures should induce a small number of system failures. We define ratio games and show that an optimal robust system corresponds to the winning strategy of a ratio game, where the system minimizes the ratio of system errors to environment errors. We show that ratio games can be solved in pseudopolynomial time
Qualitative analysis of partially-observable Markov decision processes
Get PDFWe study observation-based strategies for partially-observable Markov decision processes (POMDPs) with omega-regular objectives. An observation-based strategy relies on partial information about the history of a play, namely, on the past sequence of observa- tions. We consider the qualitative analysis problem: given a POMDP with an omega-regular objective, whether there is an observation-based strategy to achieve the objective with probability 1 (almost-sure winning), or with positive probability (positive winning). Our main results are twofold. First, we present a complete picture of the computational complexity of the qualitative analysis of POMDPs with parity objectives (a canonical form to express omega-regular objectives) and its subclasses. Our contribution consists in establishing several upper and lower bounds that were not known in literature. Second, we present optimal bounds (matching upper and lower bounds) on the memory required by pure and randomized observation-based strategies for the qualitative analysis of POMDPs with parity objectives and its subclasses
A survey of stochastic games with limsup and liminf objectives
Get PDFA stochastic game is a two-player game played oil a graph, where in each state the successor is chosen either by One of the players, or according to a probability distribution. We Survey Stochastic games with limsup and liminf objectives. A real-valued re-ward is assigned to each state, and the value of all infinite path is the limsup (resp. liminf) of all rewards along the path. The value of a stochastic game is the maximal expected value of an infinite path that call he achieved by resolving the decisions of the first player. We present the complexity of computing values of Stochastic games and their subclasses, and the complexity, of optimal strategies in such games
Formalisms for specifying Markovian population models
Get PDFWe compare several languages for specifying Markovian population models such as queuing networks and chemical reaction networks. These languages —matrix descriptions, stochastic Petri nets, stoichiometric equations, stochastic process algebras, and guarded command models— all describe continuous-time Markov chains, but they differ according to important properties, such as compositionality, expressiveness and succinctness, executability, ease of use, and the support they provide for checking the well-formedness of a model and for analyzing a model
Improved lower bounds for request-response and finitary Streett games
Get PDFWe consider two-player games played on graphs with request-response and finitary Streett objectives. We show these games are PSPACE-hard, improving the previous known NP-hardness. We also improve the lower bounds on memory required by the winning strategies for the players
Termination criteria for solving concurrent safety and reachability games
Get PDFWe consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective to stay forever in a given set of states, and its dual, the reachability objective to reach a given set of states. We present in this paper a strategy improvement algorithm for computing the value of a concurrent safety game, that is, the maximal probability with which player 1 can enforce the safety objective. The algorithm yields a sequence of player-1 strategies which ensure probabilities of winning that converge monotonically to the value of the safety game. Our result is significant because the strategy improvement algorithm provides, for the first time, a way to approximate the value of a concurrent safety game from below. Since a value iteration algorithm, or a strategy improvement algorithm for reachability games, can be used to approximate the same value from above, the combination of both algorithms yields a method for computing a converging sequence of upper and lower bounds for the values of concurrent reachability and safety games. Previous methods could approximate the values of these games only from one direction, and as no rates of convergence are known, they did not provide a practical way to solve these games
Sliding-window abstraction for infinite Markov chains
Get PDFWe present an on-the-fly abstraction technique for infinite-state continuous -time Markov chains. We consider Markov chains that are specified by a finite set of transition classes. Such models naturally represent biochemical reactions and therefore play an important role in the stochastic modeling of biological systems. We approximate the transient probability distributions at various time instances by solving a sequence of dynamically constructed abstract models, each depending on the previous one. Each abstract model is a finite Markov chain that represents the behavior of the original, infinite chain during a specific time interval. Our approach provides complete information about probability distributions, not just about individual parameters like the mean. The error of each abstraction can be computed, and the precision of the abstraction refined when desired. We implemented the algorithm and demonstrate its usefulness and efficiency on several case studies from systems biology