On restricting the ambiguity in morphic images of words

For alphabets Delta_1, Delta_2, a morphism g : Delta_1* to Delta_2* is ambiguous with respect to a word u in Delta_1* if there exists a second morphism h : Delta_1* to Delta_2* such that g(u) = h(u) and g not= h. Otherwise g is unambiguous. Hence unambiguous morphisms are those whose structure is fully preserved in their morphic images. A concept so far considered in the free monoid, the first part of this thesis considers natural extensions of ambiguity of morphisms to free groups. It is shown that, while the most straightforward generalization of ambiguity to a free monoid results in a trivial situation, that all morphisms are (always) ambiguous, there exist meaningful extensions of (un)ambiguity which are non-trivial - most notably the concepts of (un)ambiguity up to inner automorphism and up to automorphism. A characterization is given of words in a free group for which there exists an injective morphism which is unambiguous up to inner automorphism in terms of fixed points of morphisms, replicating an existing result for words in the free monoid. A conjecture is presented, which if correct, is sufficient to show an equivalent characterization for unambiguity up to automorphism. A rather counterintuitive statement is also established, that for some words, the only unambiguous (up to automorphism) morphisms are non-injective (or even periodic). The second part of the thesis addresses words for which all non-periodic morphisms are unambiguous. In the free monoid, these take the form of periodicity forcing words. It is shown using morphisms that there exist ratio-primitive periodicity forcing words over arbitrary alphabets, and furthermore that it is possible to establish large and varied classes in this way. It is observed that the set of periodicity forcing words is spanned by chains of words, where each word is a morphic image of its predecessor. It is shown that the chains terminate in exactly one direction, meaning not all periodicity forcing words may be reached as the (non-trivial) morphic image of another. Such words are called prime periodicity forcing words, and some alternative methods for finding them are given. The free-group equivalent to periodicity forcing words - a special class of C-test words - is also considered, as well as the ambiguity of terminal-preserving morphisms with respect to words containing terminal symbols, or constants. Moreover, some applications to pattern languages and group pattern languages are discussed

Doctor of Philosophy

dissertationCompilers are indispensable tools to developers. We expect them to be correct. However, compiler correctness is very hard to be reasoned about. This can be partly explained by the daunting complexity of compilers. In this dissertation, I will explain how we constructed a random program generator, Csmith, and used it to find hundreds of bugs in strong open source compilers such as the GNU Compiler Collection (GCC) and the LLVM Compiler Infrastructure (LLVM). The success of Csmith depends on its ability of being expressive and unambiguous at the same time. Csmith is composed of a code generator and a GTAV (Generation-Time Analysis and Validation) engine. They work interactively to produce expressive yet unambiguous random programs. The expressiveness of Csmith is attributed to the code generator, while the unambiguity is assured by GTAV. GTAV performs program analyses, such as points-to analysis and effect analysis, efficiently to avoid ambiguities caused by undefined behaviors or unspecifed behaviors. During our 4.25 years of testing, Csmith has found over 450 bugs in the GNU Compiler Collection (GCC) and the LLVM Compiler Infrastructure (LLVM). We analyzed the bugs by putting them into different categories, studying the root causes, finding their locations in compilers' source code, and evaluating their importance. We believe analysis results are useful to future random testers, as well as compiler writers/users

No Safe Haven for Truth Pluralists

Truth pluralism offers the latest extension in the tradition of substantive theorizing about truth. While various forms of this thesis are available, most frameworks commit to domain reliance. According to domain reliance, various ways of being true, such as coherence and correspondence, are tied to discourse domains rather than individual sentences. From this follows that the truth of different types of sentences is accounted for by their domain membership. For example, sentences addressing ethical matters are true if they cohere and those addressing extensional states of affairs if they correspond. By tying distinct truth-grounding properties to domains rather than individual sentences, truth pluralists avoid certain issues with definitional ambiguity and indeterminacy. I argue that contrary to the ideal situation, domains fail to provide the sought-after benefits of achieving definitional unambiguity and determinacy in the standard domain reliant pluralist frameworks. The reason is that, when combined with the inherently ambiguous nature of certain truth-relevant terms of sentences, fringe cases emerge, causing some of them to count as members of multiple domains. Consequently, some sentences end up being both true and false in the standard domain reliant pluralist frameworks, thus conflicting with both standard laws of non-contradiction and identity. Finally, I argue that truth pluralists should pay closer attention to the hitherto neglected question of inherent natural language ambiguity

Numbers and Languages

The thesis presents results obtained during the authors PhD-studies. First systems of language equations of a simple form consisting of just two equations are proved to be computationally universal. These are systems over unary alphabet, that are seen as systems of equations over natural numbers. The systems contain only an equation X+A=B and an equation X+X+C=X+X+D, where A, B, C and D are eventually periodic constants. It is proved that for every recursive set S there exists natural numbers p and d, and eventually periodic sets A, B, C and D such that a number n is in S if and only if np+d is in the unique solution of the abovementioned system of two equations, so all recursive sets can be represented in an encoded form. It is also proved that all recursive sets cannot be represented as they are, so the encoding is really needed. Furthermore, it is proved that the family of languages generated by Boolean grammars is closed under injective gsm-mappings and inverse gsm-mappings. The arguments apply also for the families of unambiguous Boolean languages, conjunctive languages and unambiguous languages. Finally, characterizations for morphisims preserving subfamilies of context-free languages are presented. It is shown that the families of deterministic and LL context-free languages are closed under codes if and only if they are of bounded deciphering delay. These families are also closed under non-codes, if they map every letter into a submonoid generated by a single word. The family of unambiguous context-free languages is closed under all codes and under the same non-codes as the families of deterministic and LL context-free languages.Siirretty Doriast

The syntax of Japanese nominal projections and some cross-linguistic implications

The purpose of this thesis is to examine the syntax of Japanese noun phrases and their interpretations from the cross-linguistic point of view. It has been argued that argument noun phrases contain functional heads such as D, Num(ber), and Q(uantifier) as well as a lexical projection, NP (Abney 1987; Ritter 1991, 1992, Giusti 1991, etc.) across languages. This thesis shows that argument noun phrases in Japanese can also contain heads corresponding to D, Num and Q, and that the variety of their interpretations can be explained in terms of the positions of those heads and their semantic interaction with each other. Chapter 1 outlines the theoretical background of the syntax of noun phrases and provides a review of the literature concerning Japanese noun phrases. Chapter 2 focuses on the distribution of numeral classifiers (NC) and quantifiers (Q) that can appear within noun phrases in Japanese. I propose that NC and Q can head projections, NCP and QP, and can appear either DP-internally or -externally. Chapter 3 focuses on NCs and Qs with a partitive interpretation. I argue that a partitive interpretation is obtained as the head NC or Q assigns a theta-role to its complement DP within partitive constructions. English partitive and pseudo-partitive constructions and Finnish partitives are also discussed. Chapter 4 discusses ablative partitives in Turkish and another type of partitive constructions in Japanese called the "nominal partitive constructions". I argue that a sequence of an ablative partitive and an NC in Turkish and a nominal partitive construction in Japanese are both DPs, where D takes a partitive construction, namely an NCP as its complement, giving rise to a partitive interpretation. In Chapter 5,1 demonstrate that Japanese "bare" arguments have layered structures proposed in Chapter 2, containing empty heads, i.e., D and/or NC. Four possible interpretations of bare arguments are discussed. Chapter 6 concerns predicate nominals in copular constructions. It is shown that predicate nominals in Japanese are just NPs, lacking D and NC, whereas predicate nominals in Romance and Germanic may be NPs, NumPs or DPs