Recently, we introduced a new automata model, so-called colored finite automata (CFAs) whose accepting states are multi-colored (i.e., not conventional black-and-white acceptance) in order to classify their input strings into two or more languages, and solved the specific complexity problems concerning color-unmixedness of nondeterministic CFA. That is, so-called UV, UP, and UE problems are shown to be NLOG-complete, P, and NP-complete, respectively. In this paper, we apply the concept of colored accepting mechanism to pushdown automata and show that the corresponding versions of the above-mentioned complexity problems are all undecidable. We also investigate the case of unambiguous pushdown automata and show that one of the problems turns out to be permanent true (the others remain undecidable).

A model-based mutation testing (MBMT) approach enables to perform negative testing where test cases are generated using mutant models containing intentional faults. This paper introduces an alternative MBMT framework using pushdown automata (PDA) that relate to context-free (type-2) languages. There are two key ideas in this study. One is to gain stronger representational power to capture the features whose behavior depends on previous states of software under test (SUT). The other is to make use of a relatively small test set and concentrate on suspicious parts of the SUT by using MBMT approach. Thus, the proposed framework includes (1) a novel usage of PDA for modeling SUT, (2) novel mutation operators for generating PDA mutants, (3) a novel coverage criterion, and an algorithm to generate negative test cases from mutant PDA. A case study validates the approach, and discusses its characteristics and limitations.

Visibly pushdown automata (VPA), introduced by Alur and Madhusuan in 2004, is a subclass of pushdown automata whose stack behavior is completely determined by the input symbol according to a fixed partition of the input alphabet. Since it was introduced, VPA have been shown to be useful in various contexts, e.g., as specification formalism for verification and as an automaton model for processing XML streams. However, implementation of formal verification based on VPA framework is a challenge. In this paper, we propose on-the-fly algorithms to test universality and inclusion problems of this automata class. In particular, we first present a slight improvement on the upper bound for determinization of VPA. Next, in order to check universality of a nondeterministic VPA, we simultaneously determinize this VPA and apply the P-automata technique to compute a set of reachable configurations of the target determinized VPA. When a rejecting configuration is found, the checking process stops and reports that the original VPA is not universal. Otherwise, if all configurations are accepting, the original VPA is universal. Furthermore, to strengthen the algorithm, we define a partial ordering over transitions of P-automaton, and only minimal transitions are used to incrementally generate the P-automaton. The purpose of this process is to keep the determinization step implicitly for generating reachable configurations as minimum as possible. This improvement helps to reduce not only the size of the P-automaton but also the complexity of the determinization phase. We implement the proposed algorithms in a prototype tool, named VPAchecker. Finally, we conduct experiments on randomly generated VPA. The experimental results show that the proposed method outperforms the standard one by several orders of magnitude.

One important question for quantum computing is whether a computational gap exists between models that are allowed to use quantum effects and models that are not. Several types of quantum computation models have been proposed, including quantum finite automata and quantum pushdown automata (with a quantum pushdown stack). It has been shown that some quantum computation models are more powerful than their classical counterparts and others are not since quantum computation models are required to obey such restrictions as reversible state transitions. In this paper, we investigate the power of quantum pushdown automata whose stacks are assumed to be implemented as classical devices, and show that they are strictly more powerful than their classical counterparts under the perfect-soundness condition, where perfect-soundness means that an automaton never accepts a word that is not in the language. That is, we show that our model can simulate any probabilistic pushdown automata and also show that there is a non-context-free language which quantum pushdown automata with classical stack operations can recognize with perfect soundness.

There have been many arguments that the underlying structure of natural languages is beyond the descriptive capacity of context-free languages. A well-known example is tree adjoining grammars; less common are spine grammars, linear indexed grammars, head grammars, and combinatory categorial grammars. It is known that these models of grammars have the same generative power of string languages and fall into the class of mildly context-sensitive grammars. For an automaton, it is known that the class of languages accepted by transfer pushdown automata is exactly the class of linear indexed languages. In this paper, deterministic transfer pushdown automata is introduced. We will show that the language accepted by a deterministic transfer pushdown automaton is generated by an unambiguous spine grammar. Moreover, we will show that there exists an inherently ambiguous language.

This paper investigates some fundamental properties of one-way alternating pushdown automata with sublinear space. We first show that one-way nondeterministic pushdown automata are incomparale with one-way alternating pushdown automata with only universal states, for spaces between log log n and log n, and also for spaces between log n and n/log n. We then show that there exists an infinite space hierarchy among one-way alternating pushdown automata with only universal states which have sublinear space.

This paper introduces a 1-inkdot two-way alternating pushdown automaton which is a two-way alternating pushdown automaton (2apda) with the additional power of marking at most 1 tape-cell on the input (with an inkdot) once. We first investigate a relationship between the accepting powers of sublogarithmically space-bounded 2apda's with and without 1 inkdot, and show, for example, that sublogarithmically space-bounded 2apda's with 1 inkdot are more powerful than those which have no inkdots. We next investigate an alternation hierarchy for sublogarithmically space-bounded 1-inkdot 2apda's, and show that the alternation hierarchy on the first level for 1-inkdot 2apda's holds, and we also show that 1-inkdot two-way nondeterministic pushdown automata using sublogarithmic space are incomparable with 1-inkdot two-way alternating pushdown automata with only universal states using the same space.

In this paper we introduce a bottom-up pushdown tree transducer (b-PDTT) which is a bottom-up tree transducer with pushdown storage (where the pushdown storage stores the trees) and may be considered as a dual concept of the top-down pushdown tree transducer (t-PDTT). After proving some fundamental properties of b-PDTT, for example, any b-PDTT can be realized by a linear stack with single state and converted into G-type normal form which corresponds to Greibach normal form in a context-free grammar, and so on, we compare the translational capability of a b-PDTT with that of a t-PDTT.

This paper first investigates a relationship between inkdot-depth and inkdot-size of inkdot two-way alternating Turing machines and pushdown automata with sublogarithmic space, and shows that there exists a language accepted by a strongly loglog n space-bounded alternating pushdown automaton with inkdot-depth 1, but not accepted by any weakly o (log n) space-bounded and d (n) inkdot-size bounded alternating Turing machine, for any function d (n) such that limn [d (n)log n/n1/2] = 0. In this paper, we also show that there exists an infinite space hierarchy among two-way alternating pushdown automata with sublogarithmic space.

This paper investigates the accepting powers of multi-inkdot two-way alternating pushdown automata (Turing machines) with sublogarithmic space and constant leaf-size. For each k1, and each m0, let weak-ASPACEm [L(n),k] denote the class of languages accepted by simultaneously weakly L(n) space-bounded and k leaf-bounded m-inkdot two-way alternating Turing machines, and let strong-2APDAm[L(n),k] denote the class of languages accepted by simultaneously strongly L(n) space-bounded and k leaf-bounded m-inkdot two-way alternating pushdown automata. We show that(1) strong-2APDAm [log log n,k+1]weak-ASPACEm[o(log n),k]φfor each k1 and each m1, and(2) strong-2APDA(m+1) [log log n,k]weak-ASPACEm[o(log n),k]φfor each k1 and each m0.

This paper investigates some fundamental properties of alternating one-way (or two-way) pushdown automata (pda's) with sublogarithmic space. We first show that strongly (weakly) sublogarithmic space-bounded two-way alternating pda's are more powerful than one-way alternating pda's with the same space-bound. Then, we show that weakly sublogarithmic space-bounded two-way (one-way) alternating pda's are more powerful than two-way (one-way) nondeterministic pda's and alternating pda's with only universal states using the same space, and we also show that weakly sublogarithmic space-bounded one-way nondeterministic Turing machines are incomparable with one-way alternating Turing machines with only universal states using the same space. Furthermore, we investigate several fundamental closure properties, and show that the class of languages accepted by weakly sublogarithmic space-bounded one-way alternating pda's and the class of languages accepted by sublogarithmic space-bounded two-way deterministic pda's (nondeterministic pda's, alternating pda's with only universal states) are not closed under concatenation, Kleene closure, and length preserving homomorphism. Finally, we briefly investigate a relationship between 'strongly' and 'weakly'.

In this paper, a pushdown automaton, with an infinite set of states as a partially ordered set (poset), is formulated, and its control problem of whether a given configuration can be transferred to another is discussed. For the controllability to be decidable, we take a condition the poset satisfies, that is, a condition that there are only finite number of states under the partial ordering between two given states. The control problem is decidable in polynomial time on condition the length of each pushed stack string is bounded by a constant in a given pushdown automaton. The motivation of considering the control problem comes up from the stack structure in implementing the SLD resolution deductions, in which the leftmost atom in each goal is selected and unified with some procedure name (that is, some head) of a definite clause, with the effect of the procedure name being replaced by the procedure bodies and unifications. Thus, the control problem is applied to describe the SLD resolution deductions of finite steps, by constructing a pushdown automaton model for a set of definite clauses, in which leftmost selection of atom in each goal forms a stack structure and substitutions affecting goals are interpreted as states. When constructing a pushdown automaton model for an SLD resolution deduction, algebraic properties of the idempotent substitution set, which are used in unifications, are examined and utilized. The quotient set of the idempotent substitution set per renamings is adopted to present the automaton model.