We study the relationship between the sizes of two-way finite automata accepting a language and its complement. In the deterministic case, for a given automaton (2dfa) with n states, we build an automaton accepting the complement with at most 4n states, independently of the size of the input alphabet. Actually, we show a stronger result, by presenting an equivalent 4n-state 2dfa that always hal...

We formally verify translations from two-way automata to one-way automata based on results from the literature. Following Vardi, we obtain a simple reduction from nondeterministic two-way automata to one-way automata that leads to a doubly-exponential increase in the number of states. By adapting the work of Shepherdson and Vardi, we obtain a singlyexponential translation from nondeterministic ...

We give here a simple proof of the fact that on transition systems bisimulation is the equivalence relation generated by simulation via functions. The proof entirely rests on simple rules of the calculus of relations. Simulation is a standard notion of graph homomor-phism that has been used in the study of flow diagram programs (see, e.g. [ 6,7,11]). Bisimulationis an equivalence on transition ...

We examine the succinctness of one-way, rotating, sweeping, and two-way deterministic finite automata (1dfas, rdfas, sdfas, 2dfas) and their nondeterministic and randomized counterparts. Here, a sdfa is a 2dfa whose head can change direction only on the endmarkers and a rdfa is a sdfa whose head is reset to the left end of the input every time the right end-marker is read. We study the size com...

We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata with an additional “pebble” movable along the input tape. Similarly as in the case of the classical two-way machines, it is not known whether there exists a polynomial trade-off, in the number of states, between the nondeterministic and deterministic pebble two-way automata. Ho...

A sweeping automaton is a two-way deterministic finite automaton which makes turns only at the endmarkers. Sipser [12] has proved that one-way nondeterministic finite automata can be exponentially more succinct in sizes than sweeping automata. In this paper, we propose a technique based on the work in [6] for establishing lower bounds on the size of sweeping automata. We show that Sipser’s tech...

In this thesis we investigate the relative succinctness of several types of finite automata, focusing mainly on the following four basic models: one-way deterministic (1dfas), one-way nondeterministic (1nfas), two-way deterministic (2dfas), and two-way nondeterministic (2nfas). We first establish the exact values of the trade-offs for all conversions from two-way to one-way automata. Specifical...

We should not have to look at the entire corpus (e.g., the Web) to know if two (or more) words are associated or not. A powerful sampling technique called Sketches was originally introduced to remove duplicate Web pages. We generalize sketches to estimate contingency tables and associations, using a maximum likelihood estimator to find the most likely contingency table given the sample, the mar...

This paper develops some important concepts with respect to networks and compatibility. We note that the familiar concept of complementarity lies at the heart of the concept of compatibility. We further note the distinction between two-way networks (e.g., telephones, railroads, the Internet) and one-way networks (e.g., ATMs, television, distribution and service networks). In the former, additio...