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;                                                                                                                                                                                                                                        |
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|   | 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; |
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|   | 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;                    |
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|   | 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) for the registrant and have:                                                                              |
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|   |                                                                                                                                                                                                                                                                                                                  | 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; |
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|   |                                                                                                                                                                                                                                                                                                                  | 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 |
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|   |                                                                                                                                                                                                                                                                                                                  | 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 |
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|   | 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:                                              |
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|   |                                                                                                                                                                                                                                                                                                                  | 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 |
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|   |                                                                                                                                                                                                                                                                                                                  | 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, 2004

| By:    | /s/  WILFRED J. CORRIGAN         |   |
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| Name:  | **Wilfred J. Corrigan**                    |   |
| Title: | **Chairman & Chief Executive Officer** |   |