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Exhibit 31.1 CERTIFICATION OF CHIEF EXECUTIVE OFFICER
AS ADOPTED PURSUANT TO
SECTION 302(a) OF THE SARBANES-OXLEY ACT OF 2002 I, Wilfred J. Corrigan, certify that: 1. I have reviewed this Annual Report on Form 10-K of LSI Logic Corporation; 2. Based on my knowledge, this report does not contain any untrue statement of a material fact
or omit to state a material fact necessary to make the statements made, in light of the
circumstances under which such statements were made, not misleading with respect to the period
covered by this report; 3. Based on my knowledge, the financial statements, and other financial information included in
this report, fairly present in all material respects the financial condition, results of
operations and cash flows of the registrant as of, and for, the periods presented in this
report; 4. The registrants other certifying officer and I are responsible for establishing and
maintaining disclosure controls and procedures (as defined in Exchange Act Rules 13a-15(e) and
15d-15(e)) and internal control over financial reporting (as defined in Exchange Act Rules
13a-15(f) and 15d-15(f)) for the registrant and have: a. Designed such disclosure controls and procedures, or caused such disclosure controls
and procedures to be designed under our supervision, to ensure that material information
relating to the registrant, including its consolidated subsidiaries, is made known to us
by others within those entities, particularly during the period in which this report is
being prepared; b. Designed such internal control over financial reporting, or caused such internal
control over financial reporting to be designed under our supervision, to provide
reasonable assurance regarding the reliability of financial reporting and the
preparation of financial statements for external purposes in accordance with generally
accepted accounting principles; c. Evaluated the effectiveness of the registrants disclosure controls and presented in
this report our conclusions about the effectiveness of the disclosure of controls and
procedures, as of the end of the period covered by this report based on such evaluation;
and d. Disclosed in this report any change in the registrants internal control over
financial reporting that occurred during the registrants most recent fiscal quarter
(the registrants fourth fiscal quarter in the case of an annual report) that has
materially affected, or is reasonably likely to materially affect, the registrants
internal control over financial reporting; and 5. The registrants other certifying officer and I have disclosed, based on our most recent
evaluation of internal control over financial reporting, to the registrants auditors and the
audit committee of the registrants board of directors: a. All significant deficiencies and material weakness in the design or operation of
internal controls over financial reporting which are reasonably likely to adversely
affect the registrants ability to record, process, summarize and report financial
information; and b. Any fraud, whether or not material, that involves management or other employees who
have a significant role in the registrants internal controls over financial reporting. Date:
    
    March 15, 2005By:
    
    /s/ WILFRED J. CORRIGANName:
    
    Wilfred J. CorriganTitle:
    
    Chairman & Chief Executive Officer