Preface I wrote these lecture notes during my stay in Aarhus in the academic year 1974/75. As a young researcher I had a wonderful time at DAIMI, and I have always been happy to have had that early experience. I wish to thank Heiko Vogler for his noble plan to move these notes into the digital world, and I am grateful to Florian Starke and Markus Napierkowski (and Heiko) for the excellent trans...

In this paper, two different ways of introducing alternation for lattice-valued (referred to as {L}valued)  regular tree grammars and {L}valued top-down tree automata are compared. One is the way which defines the alternating regular tree grammar, i.e., alternation is governed by the non-terminals of the grammar and the other is the way which combines state with alternation. The first way is ta...

We consider tree automata with costs over semirings in the sense of (Seidl, 1994). We define the concept of a finitely factorizing semiring and of a monotonic semiring, both as the generalization of well-known particular semirings, and show that the costfiniteness of tree automata with costs over finitely factorizing and monotonic semirings is decidable. We show that, for tree automata with cos...

μ-Calculus and automata on infinite trees are complementary ways of describing infinite tree languages. The correspondence between μ-Calculus and alternating tree automaton is used to solve the satisfiability and model checking problems by compiling the modal μ-Calculus formula into an alternating tree automata. Thus advocating an automaton model specially tailored for working with modal μ-Calc...

The model-checking problem formonadic second-order logic on graphs is fixed-parameter tractable with respect to tree-width and clique-width. The proof constructs finite deterministic automata from monadic second-order sentences, but this produces automata of hyper-exponential sizes, and this computation is not avoidable. To overcome this difficulty, we propose to consider particular monadic sec...

We present a generalized disambiguation algorithm of finite state automata, and show a proof of its correctness. This algorithm can remove ambiguities of finite state and tree automata. Our proposed algorithm can make finite state and tree automata more efficient to use in many applications.

μ-Calculus and automata on infinite trees are complementary ways of describing infinite tree languages. The correspondence between μ-Calculus and alternating tree automaton is used to solve the satisfiability and model checking problems by compiling the modal μ-Calculus formula into an alternating tree automata. Thus advocating an automaton model specially tailored for working with modal μ-Calc...

For an !-word language L, the derived tree language Path(L) is the language of trees having all their paths in L. We consider the hierarchies of deterministic automata on words and nondeterministic automata on trees with Rabin conditions in chain form. We show that L is on some level of the hierarchy of deterministic word automata ii Path(L) is on the same level of the hierarchy of nondetermini...

Automata for unranked trees form a foundation for XML schemas, querying and pattern languages. We study the problem of efficiently minimizing such automata. We start with the unranked tree automata (UTAs) that are standard in database theory, assuming bottomup determinism and that horizontal recursion is represented by deterministic finite automata. We show that minimal UTAs in that class are n...

We introduce an automata-theoretic approach for the verification of multi-agent systems. We present a translation between branching time temporal-epistemic logic and alternating tree automata. Model checking an interpreted system against a temporal-epistemic formula is reduced to checking the non-emptiness of the composition of two tree automata. We exemplify this technique using a simple multi...