TY - JOUR
AB - We solve the longstanding open problems of the blow-up involved in the translations, when possible, of a nondeterministic Büchi word automaton (NBW) to a nondeterministic co-Büchi word automaton (NCW) and to a deterministic co-Büchi word automaton (DCW). For the NBW to NCW translation, the currently known upper bound is 2o(nlog n) and the lower bound is 1.5n. We improve the upper bound to n2n and describe a matching lower bound of 2ω(n). For the NBW to DCW translation, the currently known upper bound is 2o(nlog n). We improve it to 2 o(n), which is asymptotically tight. Both of our upper-bound constructions are based on a simple subset construction, do not involve intermediate automata with richer acceptance conditions, and can be implemented symbolically. We continue and solve the open problems of translating nondeterministic Streett, Rabin, Muller, and parity word automata to NCW and to DCW. Going via an intermediate NBW is not optimal and we describe direct, simple, and asymptotically tight constructions, involving a 2o(n) blow-up. The constructions are variants of the subset construction, providing a unified approach for translating all common classes of automata to NCW and DCW. Beyond the theoretical importance of the results, we point to numerous applications of the new constructions. In particular, they imply a simple subset-construction based translation, when possible, of LTL to deterministic Büchi word automata.
AU - Boker, Udi
AU - Kupferman, Orna
ID - 494
IS - 4
JF - ACM Transactions on Computational Logic (TOCL)
TI - Translating to Co-Büchi made tight, unified, and useful
VL - 13
ER -
TY - CONF
AB - An automaton with advice is a finite state automaton which has access to an additional fixed infinite string called an advice tape. We refine the Myhill-Nerode theorem to characterize the languages of finite strings that are accepted by automata with advice. We do the same for tree automata with advice.
AU - Kruckman, Alex
AU - Rubin, Sasha
AU - Sheridan, John
AU - Zax, Ben
ID - 495
T2 - Proceedings GandALF 2012
TI - A Myhill Nerode theorem for automata with advice
VL - 96
ER -
TY - CONF
AB - We study the expressive power of logical interpretations on the class of scattered trees, namely those with countably many infinite branches. Scattered trees can be thought of as the tree analogue of scattered linear orders. Every scattered tree has an ordinal rank that reflects the structure of its infinite branches. We prove, roughly, that trees and orders of large rank cannot be interpreted in scattered trees of small rank. We consider a quite general notion of interpretation: each element of the interpreted structure is represented by a set of tuples of subsets of the interpreting tree. Our trees are countable, not necessarily finitely branching, and may have finitely many unary predicates as labellings. We also show how to replace injective set-interpretations in (not necessarily scattered) trees by 'finitary' set-interpretations.
AU - Rabinovich, Alexander
AU - Rubin, Sasha
ID - 496
TI - Interpretations in trees with countably many branches
ER -
TY - CONF
AB - One central issue in the formal design and analysis of reactive systems is the notion of refinement that asks whether all behaviors of the implementation is allowed by the specification. The local interpretation of behavior leads to the notion of simulation. Alternating transition systems (ATSs) provide a general model for composite reactive systems, and the simulation relation for ATSs is known as alternating simulation. The simulation relation for fair transition systems is called fair simulation. In this work our main contributions are as follows: (1) We present an improved algorithm for fair simulation with Büchi fairness constraints; our algorithm requires O(n 3·m) time as compared to the previous known O(n 6)-time algorithm, where n is the number of states and m is the number of transitions. (2) We present a game based algorithm for alternating simulation that requires O(m2)-time as compared to the previous known O((n·m)2)-time algorithm, where n is the number of states and m is the size of transition relation. (3) We present an iterative algorithm for alternating simulation that matches the time complexity of the game based algorithm, but is more space efficient than the game based algorithm. © Krishnendu Chatterjee, Siddhesh Chaubal, and Pritish Kamath.
AU - Chatterjee, Krishnendu
AU - Chaubal, Siddhesh
AU - Kamath, Pritish
ID - 497
TI - Faster algorithms for alternating refinement relations
VL - 16
ER -
TY - JOUR
AB - Understanding patterns and correlates of local adaptation in heterogeneous landscapes can provide important information in the selection of appropriate seed sources for restoration. We assessed the extent of local adaptation of fitness components in 12 population pairs of the perennial herb Rutidosis leptorrhynchoides (Asteraceae) and examined whether spatial scale (0.7-600 km), environmental distance, quantitative (QST) and neutral (FST) genetic differentiation, and size of the local and foreign populations could predict patterns of adaptive differentiation. Local adaptation varied among populations and fitness components. Including all population pairs, local adaptation was observed for seedling survival, but not for biomass, while foreign genotype advantage was observed for reproduction (number of inflorescences). Among population pairs, local adaptation increased with QST and local population size for biomass. QST was associated with environmental distance, suggesting ecological selection for phenotypic divergence. However, low FST and variation in population structure in small populations demonstrates the interaction of gene flow and drift in constraining local adaptation in R. leptorrhynchoides. Our study indicates that for species in heterogeneous landscapes, collecting seed from large populations from similar environments to candidate sites is likely to provide the most appropriate seed sources for restoration.
AU - Pickup, Melinda
AU - Field, David
AU - Rowell, David
AU - Young, Andrew
ID - 498
IS - 8
JF - Evolutionary Applications
TI - Predicting local adaptation in fragmented plant populations: Implications for restoration genetics
VL - 5
ER -