ω-automaton

About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.

Complexity of analysis and verification problems for communicating automata and discrete dynamical systems.

Abstract: We identify several simple but powerful concepts, techniques, and results; and we use them to characterize the complexities of a number of basic problems II, that arise in the analysis and verification of the following models M of communicating automata and discrete dynamical systems: systems of communicating automata including both finite and infinite cellular automata, transition systems, discrete dynamical systems, and succinctly-specified finite automata. These concepts, techniques, and results are centered on the following: (i) reductions Of STATE-REACHABILITY problems, especially for very simple systems of communicating copies of a single simple finite automaton, (ii) reductions of generalized CNF satisfiability problems [Sc78], especially to very simple communicating systems of copies of a few basic acyclic finite sequential machines, and (iii) reductions of the EMPTINESS and EMPTINESS-OF-INTERSECTION problems, for several kinds of regular set descriptors. For systems of communicating automata and transition systems, the problems studied include: all equivalence relations and simulation preorders in the Linear-time/Branching-time hierarchies of equivalence relations and simulation preorders of [vG90, vG93], both without and with the hiding abstraction. For discrete dynamical systems, the problems studied include the INITIAL and BOUNDARY VALUE PROBLEMS (denoted IVPs and BVPS, respectively), for nonlinear difference equations over many different algebraic structures, e.g.more » all unitary rings, all finite unitary semirings, and all lattices. For succinctly-specified finite automata, the problems studied also include the several problems studied in [AY98], e.g. the EMPTINESS, EMPTINESS-OF-INTERSECTION, EQUIVALENCE and CONTAINMENT problems. The concepts, techniques, and results presented unify and significantly extend many of the known results in the literature, e.g. [Wo86, Gu89, BPT91, GM92, Ra92, HT94, SH+96, AY98, AKY99, RH93, SM73, Hu73, HRS76, HR78], for communicating automata including both finite and infinite cellular automata and for finite automata specified by special kinds of context-free grammars, by regular operations augmented with squaring and intersection, and specified succinctly as in [AY98, AKY99]. Moreover, our development of these concepts, techniques, and results shows how several ideas, techniques, and results, for the individual models M above can be extended to apply to all or to most of these models. As one example of this and paraphrasing [BPT91] , we show: Most of these models M exhibit computationally-intractable sensitive dependence on initial conditions, for the same reason. These computationally-intractable sensitivities range from PSPACE-hard to undecidable.« less

How Powerful Are Infinite Time Machines

Abstract: We study the power of finite machines with infinite time to complete their task. To do this, we define a variant to Wojciechowski automata, investigate their recognition power, and compare them to infinite time Turing machines. Furthermore, using this infinite time, we analyse the ordinals comprehensible by such machines and discover that one can in fact go beyond the recursive realm. We conjecture that this is somehow already the case with Wojciechowski automata.

Don't Care Words with an Application to the Automata-Based Approach for Real Addition (Extended Abstract)

Abstract: Automata are a useful tool in infinite-state model checking, since they can represent infinite sets of integers and reals. However, anal- ogous to the use of bdds to represent finite sets, the sizes of the automata are an obstacle in the automata-based set representation. In this paper, we generalize the notion of "don't cares" for bdds to word languages as a means to reduce the automata sizes. We show that the minimal weak deterministic Buchi automaton (wdba) with respect to a given don't care set, under certain restrictions, is uniquely determined and can be efficiently constructed. We apply don't cares to improve the efficiency of a decision procedure for the first-order logic over the mixed linear arithmetic over the integers and the reals based on wdbas.

Reduced power automata

Abstract: We describe a class of transitive semiautomata whose power automata are reduced: any two reachable sets of states have distinct behavior. These automata appear naturally in the study of one-dimensional cellular automata.

Affine counter automata

Abstract: We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a promise problem that can be solved by exact affine counter automata but cannot be solved by deterministic counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las-Vegas affine finite automata in linear time. Lastly, we show that how a counter helps for affine finite automata by showing that the language $ \mathtt{MANYTWINS} $, which is conjectured not to be recognized by affine, quantum or classical finite state models in polynomial time, can be recognized by affine counter automata with one-sided bounded-error in realtime.