Formal series are a natural extension of formal languages by associating each word with a value called a coefficient or a weight. Among them, recognizable series and algebraic series can be regarded as extensions of regular languages and context-free languages, respectively. The coefficient of a word w can represent quantities such as the cost taken by an operation on w, the probability that w is emitted. One of the possible applications of formal series is the string counting in quantitative analysis of software. In this paper, we define the counting problems for formal series and propose algorithms for the problems. The membership problem for an automaton or a grammar corresponds to the problem of computing the coefficient of a given word in a given series. Accordingly, we define the counting problem for formal series in the following two ways. For a formal series S and a natural number d, we define CC(S,d) to be the sum of the coefficients of all the words of length d in S and SC(S,d) to be the number of words of length d that have non-zero coefficients in S. We show that for a given recognizable series S and a natural number d, CC(S,d) can be computed in O(η log d) time where η is an upper-bound of time needed for a single state-transition matrix operation, and if the state-transition matrices of S are commutative for multiplication, SC(S,d) can be computed in polynomial time of d. We extend the notions to tree series and discuss how to compute them efficiently. Also, we propose an algorithm that computes CC(S,d) in square time of d for an algebraic series S. We show the CPU time of the proposed algorithm for computing CC(S,d) for some context-free grammars as S, one of which represents the syntax of C language. To examine the applicability of the proposed algorithms to string counting for the vulnerability analysis, we also present results on string counting for Kaluza Benchmark.

String grammars (languages) have been extensively studied from 60's. On the other hand, the transformational grammar, proposed by N. Chomsky, contains the transformation from the set of derivation trees of context-free language to the surface set. And the grammar regarded a tree as an input sentence to some transducer. After that from latter half of 60's, the studies of acceptors, transducers, and so on, whose input is a tree, have been studied extensively. And recently some pushdown tree automata were introduced, and their fundamental properties and some other various properties were investigated [11]-[17]. Furthermore, a top-down pushdown tree transducer (t-PDTT for short), which is an extension of a top-down pushdown automaton (t-PDTA for short), was introduced and its fundamental properties were investigated [19]. In this paper, we define the various subclasses of context-free tree grammar (CFTG for short) by the combination of variables contained in the rules. Furthermore, we consider a monadic case of CFTG which is a special case of CFTG. Based on these definitions, we classify the subclasses of CFTG, and we investigate some inclusion properties of subclasses of CFTL (where CFTL indicates the class of context-free tree languages).

Intricate Speech Communication Mode (I-SC Mode) is observed in verbal interaction during ISDN-TV conferencing. It is characterized by conflicts and multiple interactions of speech. I-SC Mode might cause mental stress to participants and be obstacles for smooth communication. However, the reasons of I-SC Mode on the environment of information transmission are hitherto unknown. Furthermore, analyses on the talks inside a conference site (LT: local talk or a talk inside a local site) and between remote sites (MT: media talk or a talk between remote sites) are originally conceived on assumed differences in cognitive distance and media intimacy. This study deals with communication effects/barriers and cognitive distance/intimacy of media correlated with audio-video transmission signals and speech modes or talk types and response delay in human speech interactions by using an innovated conference model (decision-making transaction model: DT-Model) in synchronous ISDN-TV conference systems (SYN) and asynchronous ones (ASYN). The effects of intricate communication can be predicted to a certain extent and in some ways. In I-SC Mode, because a timely answer can not be received from recipients (or partner), response time delay and response rate are analyzed. These factors are thus analyzed with an innovated dynamic model, where the recognizable acceptance of delay is evaluated. The nonlinear model shows that the larger the response time delay, the lower the response rate becomes. Comparing the response rate between SYN and ASYN, the latter is notably lower than the former. This indicates that the communication efficiency is lower in ASYN. An I-SC Mode is the main mode that occurs during ASYN conferences, and this in turn causes psychological stress. Statistics show the prevalence of a high incidence of complicated plural talks and a low response rate exists as the main factors preventing smooth human-to-human communication. Furthermore, comparing the response delays in face-to-face LT (Tf) and machine-mediated MT (Tm), human communication delay is significantly extended by the effects of initial mechanical delays. Therefore, cognitive intimacy of media is clearly affected by the existence of physical distance.

Recognizable series is a model of a sequential machine. A recognizable series S is represented by a triple (λ,µ,γ), called a linear representation of S, where λ is a row vector of dimension n specifying the initial state, γ is a column vector of dimension n specifying the output at a state, and µ is a morphism from input words to nn matrices specifying the state transition. The output for an input word w is defined as λ(µw) γ, called the coefficient of w in S, and written as (S,w). We present an algorithm which constructs a reduced linear representation of an unknown recognizable series S, with coefficients in a commutative field, using coefficient queries and equivalence queries. The answer to a coefficient query, with a word w, is the coefficient (S, w) of w in S. When one asks an equivalence query with a linear representation (λ,µ,γ), if (λ,µ,γ) is a linear representation of S, yes is returned, and otherwise a word c such that λ (µc) γ(S, c) and the coefficient (S, c) are returned: Such a word c is called a counterexample for the query. For each execution step of the algorithm, the execution time consumed from the initial step to the current step is O(mN 4M), where N is the dimension of a reduced linear representation of S, M is the maximum time consumed by a single fundamental operation (addition, subtraction, multiplication or division), and m is the maximum length of counterexamples as answers to equivalence queries returned until that step.